Properties

Label 1900.2.l.c
Level $1900$
Weight $2$
Character orbit 1900.l
Analytic conductor $15.172$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.1715763840\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 8 x^{15} + 48 x^{14} - 184 x^{13} + 588 x^{12} - 1440 x^{11} + 3064 x^{10} - 5344 x^{9} + 8028 x^{8} - 9824 x^{7} + 9952 x^{6} - 5472 x^{5} + 1248 x^{4} + 6112 x^{3} - 4224 x^{2} + 2240 x + 5800\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{17} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of a basis \(1,\beta_1,\ldots,\beta_{15}\) for the coefficient ring described below. We also show the integral \(q\)-expansion of the trace form.

\(f(q)\) \(=\) \( q -\beta_{4} q^{3} + \beta_{9} q^{7} + ( -\beta_{2} - \beta_{11} ) q^{9} +O(q^{10})\) \( q -\beta_{4} q^{3} + \beta_{9} q^{7} + ( -\beta_{2} - \beta_{11} ) q^{9} + \beta_{6} q^{11} -\beta_{5} q^{13} -\beta_{14} q^{17} + ( \beta_{2} + \beta_{11} + \beta_{12} ) q^{19} + ( \beta_{1} - \beta_{7} ) q^{21} + ( \beta_{3} + \beta_{13} ) q^{23} + ( \beta_{8} + \beta_{10} ) q^{27} + 2 \beta_{12} q^{29} + ( \beta_{1} + \beta_{7} ) q^{31} + ( -\beta_{4} - \beta_{5} ) q^{33} + ( \beta_{8} - 2 \beta_{10} ) q^{37} + ( -2 \beta_{2} - 3 \beta_{11} ) q^{39} + ( -\beta_{1} + \beta_{7} ) q^{41} + ( \beta_{3} - \beta_{13} ) q^{43} -\beta_{9} q^{47} + ( -5 \beta_{2} - 4 \beta_{11} ) q^{49} + 2 \beta_{1} q^{51} + ( -\beta_{4} + 2 \beta_{5} ) q^{53} + ( 2 \beta_{8} - \beta_{9} - \beta_{10} + \beta_{14} ) q^{57} + ( \beta_{12} - \beta_{15} ) q^{59} + ( -2 + 3 \beta_{6} ) q^{61} + ( \beta_{3} + 3 \beta_{13} ) q^{63} + ( -4 \beta_{8} - \beta_{10} ) q^{67} + ( 3 \beta_{12} + \beta_{15} ) q^{69} + ( \beta_{1} - \beta_{7} ) q^{71} -2 \beta_{3} q^{73} + ( 2 \beta_{9} - \beta_{14} ) q^{77} + ( \beta_{12} + \beta_{15} ) q^{79} + ( 5 + \beta_{6} ) q^{81} + ( -2 \beta_{3} + 3 \beta_{13} ) q^{83} + ( -2 \beta_{9} + 2 \beta_{14} ) q^{87} + 2 \beta_{12} q^{89} + ( 3 \beta_{1} - \beta_{7} ) q^{91} + ( \beta_{3} - 4 \beta_{13} ) q^{93} + ( 5 \beta_{8} + 2 \beta_{10} ) q^{97} + ( -6 \beta_{2} - \beta_{11} ) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + O(q^{10}) \) \( 16q - 32q^{61} + 80q^{81} + O(q^{100}) \)

Basis of coefficient ring in terms of a root \(\nu\) of \(x^{16} - 8 x^{15} + 48 x^{14} - 184 x^{13} + 588 x^{12} - 1440 x^{11} + 3064 x^{10} - 5344 x^{9} + 8028 x^{8} - 9824 x^{7} + 9952 x^{6} - 5472 x^{5} + 1248 x^{4} + 6112 x^{3} - 4224 x^{2} + 2240 x + 5800\):

\(\beta_{0}\)\(=\)\( 1 \)
\(\beta_{1}\)\(=\)\((\)\(3404742364 \nu^{15} - 63834217534 \nu^{14} + 427804418714 \nu^{13} - 2161411700658 \nu^{12} + 7483730081226 \nu^{11} - 21885664557003 \nu^{10} + 49764674507880 \nu^{9} - 99799751236626 \nu^{8} + 164329990339240 \nu^{7} - 232108303110496 \nu^{6} + 273604667036836 \nu^{5} - 254258226272226 \nu^{4} + 130941498846960 \nu^{3} - 64558098021052 \nu^{2} - 62190295761940 \nu + 9822248453700\)\()/ 45470877735650 \)
\(\beta_{2}\)\(=\)\((\)\(603090818534 \nu^{15} - 5243849724144 \nu^{14} + 31506273291774 \nu^{13} - 118945960487813 \nu^{12} + 353600813370636 \nu^{11} - 759161813920578 \nu^{10} + 1326469653581160 \nu^{9} - 1647594492343731 \nu^{8} + 1388959248339600 \nu^{7} + 392072217254624 \nu^{6} - 3860268726845424 \nu^{5} + 8221950715209684 \nu^{4} - 10491219595987480 \nu^{3} + 9364859921510088 \nu^{2} + 2506553050513680 \nu - 5101176041372150\)\()/ 7411753070910950 \)
\(\beta_{3}\)\(=\)\((\)\(-129262203733548 \nu^{15} + 1452541075486068 \nu^{14} - 8691915185839763 \nu^{13} + 36312587722455051 \nu^{12} - 107932211056469872 \nu^{11} + 253626745551224301 \nu^{10} - 441663983408706740 \nu^{9} + 596943581202812487 \nu^{8} - 460685512848646940 \nu^{7} - 334482057543612268 \nu^{6} + 1766697690571686548 \nu^{5} - 4017734202407725518 \nu^{4} + 5599710570398387380 \nu^{3} - 4584602523612127256 \nu^{2} + 2896267920455124000 \nu + 651331584869104200\)\()/ 996880788037522775 \)
\(\beta_{4}\)\(=\)\((\)\(-608903147273088 \nu^{15} + 5182475086402038 \nu^{14} - 34668638177110088 \nu^{13} + 147484296826840631 \nu^{12} - 522769100695815382 \nu^{11} + 1394992380801573356 \nu^{10} - 3178745760226392710 \nu^{9} + 5800798929349851812 \nu^{8} - 9127698403251020080 \nu^{7} + 11853664204502581372 \nu^{6} - 12371848971989044572 \nu^{5} + 8152273999188653452 \nu^{4} - 2275969854679100680 \nu^{3} - 8036160163201717596 \nu^{2} + 4632703292697345440 \nu + 2885963899977715400\)\()/ 3987523152150091100 \)
\(\beta_{5}\)\(=\)\((\)\(631490110904546 \nu^{15} - 4780612860471596 \nu^{14} + 25782364013875596 \nu^{13} - 88281219473488427 \nu^{12} + 255948188927617194 \nu^{11} - 609674312376184802 \nu^{10} + 1416254709450494070 \nu^{9} - 2989652443786969804 \nu^{8} + 5761163684198880560 \nu^{7} - 9087503461182255224 \nu^{6} + 13021776441583581124 \nu^{5} - 14396876042005434984 \nu^{4} + 12437632446385645360 \nu^{3} - 9041051695899477268 \nu^{2} - 4243816664234853480 \nu + 15857699233954043200\)\()/ 3987523152150091100 \)
\(\beta_{6}\)\(=\)\((\)\(-5747364 \nu^{15} + 51262207 \nu^{14} - 315413196 \nu^{13} + 1294440423 \nu^{12} - 4232991322 \nu^{11} + 10934282618 \nu^{10} - 23435959384 \nu^{9} + 42225384687 \nu^{8} - 62166364024 \nu^{7} + 76785126764 \nu^{6} - 71346710340 \nu^{5} + 38737859810 \nu^{4} + 9209797480 \nu^{3} - 61389569044 \nu^{2} + 73253204040 \nu + 14137291952\)\()/ 27146792678 \)
\(\beta_{7}\)\(=\)\((\)\(2482704232 \nu^{15} - 6162325547 \nu^{14} + 33239984062 \nu^{13} + 3359208941 \nu^{12} + 99837424838 \nu^{11} + 34991525051 \nu^{10} + 1601865568610 \nu^{9} - 4143520538238 \nu^{8} + 12883561429120 \nu^{7} - 24419211093988 \nu^{6} + 42026106792168 \nu^{5} - 45550339116658 \nu^{4} + 80487671746880 \nu^{3} - 14209161729696 \nu^{2} + 31563591254580 \nu + 45411323499100\)\()/ 9094175547130 \)
\(\beta_{8}\)\(=\)\((\)\(-1125818137415556 \nu^{15} + 7850899553324166 \nu^{14} - 42818703704656306 \nu^{13} + 137758199514538867 \nu^{12} - 379546990085498774 \nu^{11} + 735140884486446502 \nu^{10} - 1314011089149128970 \nu^{9} + 1778262068917099364 \nu^{8} - 2156671466819310360 \nu^{7} + 1699935543790946004 \nu^{6} - 1430679264620539924 \nu^{5} - 334078665547978816 \nu^{4} - 1720759582468429920 \nu^{3} + 1532863573019504068 \nu^{2} - 9450817124369083960 \nu - 3423558891959354600\)\()/ 3987523152150091100 \)
\(\beta_{9}\)\(=\)\((\)\(628431571537036 \nu^{15} - 1767667613603051 \nu^{14} + 5445385002781226 \nu^{13} + 22626137854128428 \nu^{12} - 115142450366717066 \nu^{11} + 493573060975492808 \nu^{10} - 1126710992174377600 \nu^{9} + 2396119992967862036 \nu^{8} - 3913463266497023780 \nu^{7} + 5330615214380948616 \nu^{6} - 5355369663046646956 \nu^{5} + 5943014528351290196 \nu^{4} + 1439591763157443320 \nu^{3} + 29352698236217212 \nu^{2} + 3512718831325279640 \nu + 574275189258608500\)\()/ 1993761576075045550 \)
\(\beta_{10}\)\(=\)\((\)\(1334440048083898 \nu^{15} - 8566841047955378 \nu^{14} + 43437284569896498 \nu^{13} - 115506473056966111 \nu^{12} + 245045438670892842 \nu^{11} - 176056066195378016 \nu^{10} - 253706661867182790 \nu^{9} + 1893563535975679288 \nu^{8} - 4562866168067405520 \nu^{7} + 9275325100660669568 \nu^{6} - 12392158324829254108 \nu^{5} + 16976086838061143628 \nu^{4} - 11920592500955642840 \nu^{3} + 10139955343076398156 \nu^{2} + 6767279472519777680 \nu + 9336430308432196800\)\()/ 3987523152150091100 \)
\(\beta_{11}\)\(=\)\((\)\(4176 \nu^{15} - 37891 \nu^{14} + 232586 \nu^{13} - 934932 \nu^{12} + 2974454 \nu^{11} - 7309692 \nu^{10} + 15117340 \nu^{9} - 25921809 \nu^{8} + 38402400 \nu^{7} - 46692064 \nu^{6} + 47449964 \nu^{5} - 31058674 \nu^{4} + 13293280 \nu^{3} + 13400132 \nu^{2} + 6810520 \nu - 805100\)\()/10374950\)
\(\beta_{12}\)\(=\)\((\)\(2166898748 \nu^{15} - 15097277260 \nu^{14} + 80885054370 \nu^{13} - 256170024905 \nu^{12} + 677613701850 \nu^{11} - 1241080563907 \nu^{10} + 1960024793014 \nu^{9} - 2136711657276 \nu^{8} + 1319316240768 \nu^{7} + 1464714515932 \nu^{6} - 3906847382540 \nu^{5} + 8790182307278 \nu^{4} - 2827755828648 \nu^{3} - 4062373486800 \nu^{2} + 10577327553900 \nu - 11035714715932\)\()/ 4424927206514 \)
\(\beta_{13}\)\(=\)\((\)\(-1120501569223378 \nu^{15} + 10765761131244873 \nu^{14} - 64241368589123968 \nu^{13} + 259652539992778936 \nu^{12} - 795898321119354842 \nu^{11} + 1938438371778676686 \nu^{10} - 3803959900260759740 \nu^{9} + 6411948787323872382 \nu^{8} - 8799901394433328540 \nu^{7} + 10099202088850783452 \nu^{6} - 8655427339934971172 \nu^{5} + 3726934266787856652 \nu^{4} + 3289760888113268480 \nu^{3} - 2073572915755703716 \nu^{2} + 3502601476216977000 \nu + 6861853613740563700\)\()/ 1993761576075045550 \)
\(\beta_{14}\)\(=\)\((\)\(-705129212158676 \nu^{15} + 5106091744068366 \nu^{14} - 30268483425395991 \nu^{13} + 110624784799468052 \nu^{12} - 356039426593955994 \nu^{11} + 860852104699374447 \nu^{10} - 1889558087874428800 \nu^{9} + 3346327580693011949 \nu^{8} - 5268554897231812820 \nu^{7} + 6882267300588257544 \nu^{6} - 7939676405826211304 \nu^{5} + 6120802409211742314 \nu^{4} - 4820502789894397420 \nu^{3} - 732500976204893092 \nu^{2} + 2252729006902401760 \nu - 3634775427194973500\)\()/ 996880788037522775 \)
\(\beta_{15}\)\(=\)\((\)\(10709177408 \nu^{15} - 79061811993 \nu^{14} + 439445786448 \nu^{13} - 1512144077948 \nu^{12} + 4335120362722 \nu^{11} - 9322649086621 \nu^{10} + 17567291876368 \nu^{9} - 27369480290760 \nu^{8} + 35481517487880 \nu^{7} - 36707364043988 \nu^{6} + 29994055278224 \nu^{5} + 1729790299958 \nu^{4} - 9506328966600 \nu^{3} + 23912465504732 \nu^{2} - 14245987732620 \nu + 179749858580\)\()/ 4424927206514 \)
\(1\)\(=\)\(\beta_0\)
\(\nu\)\(=\)\((\)\(\beta_{14} - 2 \beta_{8} - 2 \beta_{4} - 2 \beta_{2} + 2\)\()/4\)
\(\nu^{2}\)\(=\)\((\)\(\beta_{14} - 2 \beta_{12} + 2 \beta_{11} - 4 \beta_{8} - 2 \beta_{6} - \beta_{3} - 8 \beta_{2} - 2 \beta_{1} - 8\)\()/4\)
\(\nu^{3}\)\(=\)\((\)\(-3 \beta_{14} + \beta_{13} - 6 \beta_{12} + 6 \beta_{11} - 4 \beta_{10} + 3 \beta_{9} - 4 \beta_{8} - 2 \beta_{5} + 14 \beta_{4} - 4 \beta_{3} + 2 \beta_{2} - 22\)\()/4\)
\(\nu^{4}\)\(=\)\(\beta_{15} - 3 \beta_{14} + 2 \beta_{13} - 2 \beta_{12} - \beta_{10} + \beta_{9} + 5 \beta_{8} + 5 \beta_{6} - 3 \beta_{5} + 7 \beta_{4} + 15 \beta_{2} + 5 \beta_{1} - 3\)
\(\nu^{5}\)\(=\)\((\)\(10 \beta_{15} - 13 \beta_{14} + 10 \beta_{13} + 30 \beta_{12} - 50 \beta_{11} + 34 \beta_{10} - 28 \beta_{9} + 90 \beta_{8} + 10 \beta_{7} + 30 \beta_{6} - 34 \beta_{5} - 10 \beta_{4} + 35 \beta_{3} + 108 \beta_{2} + 50 \beta_{1} + 112\)\()/4\)
\(\nu^{6}\)\(=\)\((\)\(-13 \beta_{15} + 32 \beta_{14} - 37 \beta_{13} + 79 \beta_{12} - 72 \beta_{11} + 72 \beta_{10} - 37 \beta_{9} + 54 \beta_{8} + 23 \beta_{7} - 66 \beta_{6} + 10 \beta_{5} - 100 \beta_{4} + 43 \beta_{3} - 62 \beta_{2} - \beta_{1} + 206\)\()/2\)
\(\nu^{7}\)\(=\)\((\)\(-91 \beta_{15} + 161 \beta_{14} - 138 \beta_{13} + 112 \beta_{12} + 70 \beta_{11} + 79 \beta_{10} + 84 \beta_{9} - 139 \beta_{8} - 308 \beta_{6} + 215 \beta_{5} - 251 \beta_{4} - 14 \beta_{3} - 552 \beta_{2} - 175 \beta_{1} + 176\)\()/2\)
\(\nu^{8}\)\(=\)\(-56 \beta_{15} + 120 \beta_{14} + 46 \beta_{13} - 112 \beta_{12} + 490 \beta_{11} - 216 \beta_{10} + 262 \beta_{9} - 360 \beta_{8} - 132 \beta_{7} - 110 \beta_{6} + 280 \beta_{5} - 32 \beta_{4} - 202 \beta_{3} - 630 \beta_{2} - 260 \beta_{1} - 458\)
\(\nu^{9}\)\(=\)\((\)\(600 \beta_{15} - 573 \beta_{14} + 1590 \beta_{13} - 1500 \beta_{12} + 2124 \beta_{11} - 2144 \beta_{10} + 318 \beta_{9} - 1268 \beta_{8} - 684 \beta_{7} + 2376 \beta_{6} - 316 \beta_{5} + 1372 \beta_{4} - 1275 \beta_{3} - 172 \beta_{2} - 360 \beta_{1} - 4088\)\()/2\)
\(\nu^{10}\)\(=\)\(1334 \beta_{15} - 2032 \beta_{14} + 1398 \beta_{13} - 1728 \beta_{12} - 1662 \beta_{11} - 1258 \beta_{10} - 2052 \beta_{9} + 240 \beta_{8} + 376 \beta_{7} + 4592 \beta_{6} - 3090 \beta_{5} + 2400 \beta_{4} - 443 \beta_{3} + 4108 \beta_{2} + 1392 \beta_{1} - 3872\)
\(\nu^{11}\)\(=\)\((\)\(1562 \beta_{15} - 9339 \beta_{14} - 7746 \beta_{13} - 88 \beta_{12} - 29370 \beta_{11} + 12374 \beta_{10} - 12496 \beta_{9} + 10686 \beta_{8} + 8250 \beta_{7} + 4642 \beta_{6} - 16070 \beta_{5} + 8574 \beta_{4} + 8425 \beta_{3} + 32308 \beta_{2} + 13200 \beta_{1} + 1816\)\()/2\)
\(\nu^{12}\)\(=\)\(-9826 \beta_{15} + 2116 \beta_{14} - 21346 \beta_{13} + 15958 \beta_{12} - 27390 \beta_{11} + 30464 \beta_{10} + 2734 \beta_{9} + 21260 \beta_{8} + 7658 \beta_{7} - 34998 \beta_{6} + 3652 \beta_{5} - 2008 \beta_{4} + 19144 \beta_{3} + 31680 \beta_{2} + 12770 \beta_{1} + 38844\)
\(\nu^{13}\)\(=\)\(-33280 \beta_{15} + 52204 \beta_{14} - 19175 \beta_{13} + 63180 \beta_{12} + 50310 \beta_{11} + 37688 \beta_{10} + 58885 \beta_{9} + 43046 \beta_{8} - 14950 \beta_{7} - 121420 \beta_{6} + 83862 \beta_{5} - 57444 \beta_{4} + 28535 \beta_{3} - 28698 \beta_{2} - 15470 \beta_{1} + 161818\)
\(\nu^{14}\)\(=\)\(-8154 \beta_{15} + 165389 \beta_{14} + 126260 \beta_{13} + 79252 \beta_{12} + 381238 \beta_{11} - 154322 \beta_{10} + 121710 \beta_{9} - 62482 \beta_{8} - 105076 \beta_{7} - 49738 \beta_{6} + 226070 \beta_{5} - 240890 \beta_{4} - 83489 \beta_{3} - 487912 \beta_{2} - 193618 \beta_{1} + 255148\)
\(\nu^{15}\)\(=\)\(249607 \beta_{15} + 72423 \beta_{14} + 461244 \beta_{13} - 367639 \beta_{12} + 686394 \beta_{11} - 809454 \beta_{10} - 162528 \beta_{9} - 800040 \beta_{8} - 167375 \beta_{7} + 877890 \beta_{6} - 34316 \beta_{5} - 305230 \beta_{4} - 573471 \beta_{3} - 1648932 \beta_{2} - 567125 \beta_{1} - 843668\)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\) \(951\)
\(\chi(n)\) \(-\beta_{2}\) \(-1\) \(1\)

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
493.1
0.870982 + 0.924776i
0.129018 + 1.66674i
−0.667207 + 1.54769i
1.66721 0.786721i
−0.667207 0.213279i
1.66721 2.54769i
0.870982 2.66674i
0.129018 1.92478i
0.870982 0.924776i
0.129018 1.66674i
−0.667207 1.54769i
1.66721 + 0.786721i
−0.667207 + 0.213279i
1.66721 + 2.54769i
0.870982 + 2.66674i
0.129018 + 1.92478i
0 −1.79576 + 1.79576i 0 0 0 −3.30136 + 3.30136i 0 3.44949i 0
493.2 0 −1.79576 + 1.79576i 0 0 0 3.30136 3.30136i 0 3.44949i 0
493.3 0 −0.880486 + 0.880486i 0 0 0 −1.04930 + 1.04930i 0 1.44949i 0
493.4 0 −0.880486 + 0.880486i 0 0 0 1.04930 1.04930i 0 1.44949i 0
493.5 0 0.880486 0.880486i 0 0 0 −1.04930 + 1.04930i 0 1.44949i 0
493.6 0 0.880486 0.880486i 0 0 0 1.04930 1.04930i 0 1.44949i 0
493.7 0 1.79576 1.79576i 0 0 0 −3.30136 + 3.30136i 0 3.44949i 0
493.8 0 1.79576 1.79576i 0 0 0 3.30136 3.30136i 0 3.44949i 0
1557.1 0 −1.79576 1.79576i 0 0 0 −3.30136 3.30136i 0 3.44949i 0
1557.2 0 −1.79576 1.79576i 0 0 0 3.30136 + 3.30136i 0 3.44949i 0
1557.3 0 −0.880486 0.880486i 0 0 0 −1.04930 1.04930i 0 1.44949i 0
1557.4 0 −0.880486 0.880486i 0 0 0 1.04930 + 1.04930i 0 1.44949i 0
1557.5 0 0.880486 + 0.880486i 0 0 0 −1.04930 1.04930i 0 1.44949i 0
1557.6 0 0.880486 + 0.880486i 0 0 0 1.04930 + 1.04930i 0 1.44949i 0
1557.7 0 1.79576 + 1.79576i 0 0 0 −3.30136 3.30136i 0 3.44949i 0
1557.8 0 1.79576 + 1.79576i 0 0 0 3.30136 + 3.30136i 0 3.44949i 0
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1557.8
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
5.c odd 4 2 inner
19.b odd 2 1 inner
95.d odd 2 1 inner
95.g even 4 2 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1900.2.l.c 16
5.b even 2 1 inner 1900.2.l.c 16
5.c odd 4 2 inner 1900.2.l.c 16
19.b odd 2 1 inner 1900.2.l.c 16
95.d odd 2 1 inner 1900.2.l.c 16
95.g even 4 2 inner 1900.2.l.c 16
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1900.2.l.c 16 1.a even 1 1 trivial
1900.2.l.c 16 5.b even 2 1 inner
1900.2.l.c 16 5.c odd 4 2 inner
1900.2.l.c 16 19.b odd 2 1 inner
1900.2.l.c 16 95.d odd 2 1 inner
1900.2.l.c 16 95.g even 4 2 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{8} + 44 T_{3}^{4} + 100 \) acting on \(S_{2}^{\mathrm{new}}(1900, [\chi])\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T^{16} \)
$3$ \( ( 100 + 44 T^{4} + T^{8} )^{2} \)
$5$ \( T^{16} \)
$7$ \( ( 2304 + 480 T^{4} + T^{8} )^{2} \)
$11$ \( ( -6 + T^{2} )^{8} \)
$13$ \( ( 62500 + 524 T^{4} + T^{8} )^{2} \)
$17$ \( ( 36864 + 1920 T^{4} + T^{8} )^{2} \)
$19$ \( ( 130321 - 7220 T^{2} + 438 T^{4} - 20 T^{6} + T^{8} )^{2} \)
$23$ \( ( 1440000 + 2784 T^{4} + T^{8} )^{2} \)
$29$ \( ( 1920 - 96 T^{2} + T^{4} )^{4} \)
$31$ \( ( 4320 + 144 T^{2} + T^{4} )^{4} \)
$37$ \( ( 27984100 + 12524 T^{4} + T^{8} )^{2} \)
$41$ \( ( 480 + 144 T^{2} + T^{4} )^{4} \)
$43$ \( ( 186624 + 4320 T^{4} + T^{8} )^{2} \)
$47$ \( ( 2304 + 480 T^{4} + T^{8} )^{2} \)
$53$ \( ( 5062500 + 9900 T^{4} + T^{8} )^{2} \)
$59$ \( ( 4320 - 144 T^{2} + T^{4} )^{4} \)
$61$ \( ( -50 + 4 T + T^{2} )^{8} \)
$67$ \( ( 13032100 + 9164 T^{4} + T^{8} )^{2} \)
$71$ \( ( 480 + 144 T^{2} + T^{4} )^{4} \)
$73$ \( ( 9437184 + 30720 T^{4} + T^{8} )^{2} \)
$79$ \( ( 480 - 144 T^{2} + T^{4} )^{4} \)
$83$ \( ( 900000000 + 106464 T^{4} + T^{8} )^{2} \)
$89$ \( ( 1920 - 96 T^{2} + T^{4} )^{4} \)
$97$ \( ( 39062500 + 49004 T^{4} + T^{8} )^{2} \)
show more
show less