Properties

Label 183.2.a
Level 183
Weight 2
Character orbit a
Rep. character \(\chi_{183}(1,\cdot)\)
Character field \(\Q\)
Dimension 11
Newform subspaces 3
Sturm bound 41
Trace bound 1

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Defining parameters

Level: \( N \) = \( 183 = 3 \cdot 61 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 183.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(41\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(183))\).

Total New Old
Modular forms 22 11 11
Cusp forms 19 11 8
Eisenstein series 3 0 3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)\(61\)FrickeDim.
\(+\)\(+\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(6\)
Plus space\(+\)\(2\)
Minus space\(-\)\(9\)

Trace form

\( 11q - q^{2} + q^{3} + 13q^{4} + 6q^{5} + q^{6} - 9q^{8} + 11q^{9} + O(q^{10}) \) \( 11q - q^{2} + q^{3} + 13q^{4} + 6q^{5} + q^{6} - 9q^{8} + 11q^{9} - 2q^{10} - 8q^{11} + 7q^{12} + 6q^{13} - 16q^{14} - 2q^{15} + 13q^{16} + 10q^{17} - q^{18} + 4q^{19} - 6q^{20} + 4q^{21} - 16q^{22} - 3q^{24} + 9q^{25} - 2q^{26} + q^{27} - 8q^{28} - 6q^{29} - 10q^{30} - 4q^{31} - 9q^{32} - 8q^{33} - 6q^{34} - 12q^{35} + 13q^{36} - 14q^{37} + 12q^{38} + 6q^{39} - 42q^{40} - 14q^{41} - 20q^{42} + 16q^{43} - 48q^{44} + 6q^{45} - 20q^{46} - 8q^{47} + 7q^{48} + 15q^{49} + 5q^{50} + 10q^{51} + 26q^{52} + 6q^{53} + q^{54} - 4q^{55} - 40q^{56} + 12q^{57} - 10q^{58} - 20q^{59} - 6q^{60} - 5q^{61} + 28q^{62} + 5q^{64} + 16q^{65} - 4q^{66} + 4q^{67} + 38q^{68} + 12q^{70} + 8q^{71} - 9q^{72} + 18q^{73} + 42q^{74} + 31q^{75} - 60q^{76} + 44q^{77} - 10q^{78} - 8q^{79} + 18q^{80} + 11q^{81} + 50q^{82} - 28q^{83} + 4q^{84} + 28q^{85} - 56q^{86} - 14q^{87} + 6q^{89} - 2q^{90} - 20q^{91} + 32q^{92} + 4q^{93} - 32q^{94} - 56q^{95} - 15q^{96} + 22q^{97} + 51q^{98} - 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(183))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 61
183.2.a.a \(2\) \(1.461\) \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(-2\) \(-2\) \(+\) \(+\) \(q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}-q^{5}+\cdots\)
183.2.a.b \(3\) \(1.461\) 3.3.148.1 None \(1\) \(-3\) \(6\) \(0\) \(+\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}+2q^{5}+\cdots\)
183.2.a.c \(6\) \(1.461\) 6.6.91407488.1 None \(0\) \(6\) \(2\) \(2\) \(-\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+(1+\beta _{3}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(183))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(183)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(61))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 2 T + 3 T^{2} + 4 T^{3} + 4 T^{4} \))(\( 1 - T + 3 T^{2} - 3 T^{3} + 6 T^{4} - 4 T^{5} + 8 T^{6} \))(\( 1 + T^{2} + 2 T^{3} + 3 T^{4} + 2 T^{5} + 3 T^{6} + 4 T^{7} + 12 T^{8} + 16 T^{9} + 16 T^{10} + 64 T^{12} \))
$3$ (\( ( 1 + T )^{2} \))(\( ( 1 + T )^{3} \))(\( ( 1 - T )^{6} \))
$5$ (\( ( 1 + T + 5 T^{2} )^{2} \))(\( ( 1 - 2 T + 5 T^{2} )^{3} \))(\( 1 - 2 T + 7 T^{2} - 22 T^{3} + 59 T^{4} - 160 T^{5} + 346 T^{6} - 800 T^{7} + 1475 T^{8} - 2750 T^{9} + 4375 T^{10} - 6250 T^{11} + 15625 T^{12} \))
$7$ (\( 1 + 2 T + 13 T^{2} + 14 T^{3} + 49 T^{4} \))(\( 1 + 5 T^{2} - 16 T^{3} + 35 T^{4} + 343 T^{6} \))(\( 1 - 2 T + 17 T^{2} - 10 T^{3} + 163 T^{4} - 152 T^{5} + 1590 T^{6} - 1064 T^{7} + 7987 T^{8} - 3430 T^{9} + 40817 T^{10} - 33614 T^{11} + 117649 T^{12} \))
$11$ (\( 1 + 2 T + 21 T^{2} + 22 T^{3} + 121 T^{4} \))(\( 1 - 2 T + 29 T^{2} - 40 T^{3} + 319 T^{4} - 242 T^{5} + 1331 T^{6} \))(\( 1 + 8 T + 61 T^{2} + 330 T^{3} + 1527 T^{4} + 6058 T^{5} + 21498 T^{6} + 66638 T^{7} + 184767 T^{8} + 439230 T^{9} + 893101 T^{10} + 1288408 T^{11} + 1771561 T^{12} \))
$13$ (\( ( 1 + 3 T + 13 T^{2} )^{2} \))(\( 1 - 6 T + 35 T^{2} - 116 T^{3} + 455 T^{4} - 1014 T^{5} + 2197 T^{6} \))(\( 1 - 6 T + 55 T^{2} - 274 T^{3} + 1507 T^{4} - 6080 T^{5} + 24378 T^{6} - 79040 T^{7} + 254683 T^{8} - 601978 T^{9} + 1570855 T^{10} - 2227758 T^{11} + 4826809 T^{12} \))
$17$ (\( ( 1 + 6 T + 17 T^{2} )^{2} \))(\( 1 - 12 T + 71 T^{2} - 308 T^{3} + 1207 T^{4} - 3468 T^{5} + 4913 T^{6} \))(\( 1 - 10 T + 90 T^{2} - 482 T^{3} + 2835 T^{4} - 12484 T^{5} + 60164 T^{6} - 212228 T^{7} + 819315 T^{8} - 2368066 T^{9} + 7516890 T^{10} - 14198570 T^{11} + 24137569 T^{12} \))
$19$ (\( 1 - 4 T + 10 T^{2} - 76 T^{3} + 361 T^{4} \))(\( 1 + 8 T + 65 T^{2} + 288 T^{3} + 1235 T^{4} + 2888 T^{5} + 6859 T^{6} \))(\( 1 - 8 T + 54 T^{2} - 104 T^{3} + 263 T^{4} + 1280 T^{5} + 532 T^{6} + 24320 T^{7} + 94943 T^{8} - 713336 T^{9} + 7037334 T^{10} - 19808792 T^{11} + 47045881 T^{12} \))
$23$ (\( 1 + 2 T + 29 T^{2} + 46 T^{3} + 529 T^{4} \))(\( 1 - 2 T + 25 T^{2} - 72 T^{3} + 575 T^{4} - 1058 T^{5} + 12167 T^{6} \))(\( 1 + 93 T^{2} + 2 T^{3} + 4215 T^{4} + 346 T^{5} + 119626 T^{6} + 7958 T^{7} + 2229735 T^{8} + 24334 T^{9} + 26025213 T^{10} + 148035889 T^{12} \))
$29$ (\( 1 + 26 T^{2} + 841 T^{4} \))(\( 1 - 4 T + 83 T^{2} - 212 T^{3} + 2407 T^{4} - 3364 T^{5} + 24389 T^{6} \))(\( 1 + 10 T + 118 T^{2} + 618 T^{3} + 4379 T^{4} + 15748 T^{5} + 114652 T^{6} + 456692 T^{7} + 3682739 T^{8} + 15072402 T^{9} + 83459158 T^{10} + 205111490 T^{11} + 594823321 T^{12} \))
$31$ (\( 1 - 4 T + 34 T^{2} - 124 T^{3} + 961 T^{4} \))(\( 1 + 8 T + 61 T^{2} + 224 T^{3} + 1891 T^{4} + 7688 T^{5} + 29791 T^{6} \))(\( 1 + 78 T^{2} + 256 T^{3} + 3039 T^{4} + 15680 T^{5} + 105380 T^{6} + 486080 T^{7} + 2920479 T^{8} + 7626496 T^{9} + 72034638 T^{10} + 887503681 T^{12} \))
$37$ (\( 1 + 4 T + 70 T^{2} + 148 T^{3} + 1369 T^{4} \))(\( 1 + 6 T + 59 T^{2} + 452 T^{3} + 2183 T^{4} + 8214 T^{5} + 50653 T^{6} \))(\( 1 + 4 T + 98 T^{2} + 324 T^{3} + 4279 T^{4} + 13768 T^{5} + 142140 T^{6} + 509416 T^{7} + 5857951 T^{8} + 16411572 T^{9} + 183667778 T^{10} + 277375828 T^{11} + 2565726409 T^{12} \))
$41$ (\( 1 + 6 T + 83 T^{2} + 246 T^{3} + 1681 T^{4} \))(\( 1 - 2 T + 87 T^{2} - 60 T^{3} + 3567 T^{4} - 3362 T^{5} + 68921 T^{6} \))(\( 1 + 10 T + 191 T^{2} + 1350 T^{3} + 16051 T^{4} + 89568 T^{5} + 814746 T^{6} + 3672288 T^{7} + 26981731 T^{8} + 93043350 T^{9} + 539720351 T^{10} + 1158562010 T^{11} + 4750104241 T^{12} \))
$43$ (\( 1 - 12 T + 90 T^{2} - 516 T^{3} + 1849 T^{4} \))(\( 1 + 9 T^{2} + 16 T^{3} + 387 T^{4} + 79507 T^{6} \))(\( 1 - 4 T + 206 T^{2} - 684 T^{3} + 19303 T^{4} - 52984 T^{5} + 1058436 T^{6} - 2278312 T^{7} + 35691247 T^{8} - 54382788 T^{9} + 704273006 T^{10} - 588033772 T^{11} + 6321363049 T^{12} \))
$47$ (\( 1 + 8 T + 38 T^{2} + 376 T^{3} + 2209 T^{4} \))(\( 1 - 4 T + 93 T^{2} - 312 T^{3} + 4371 T^{4} - 8836 T^{5} + 103823 T^{6} \))(\( 1 + 4 T + 178 T^{2} + 908 T^{3} + 15631 T^{4} + 83848 T^{5} + 881340 T^{6} + 3940856 T^{7} + 34528879 T^{8} + 94271284 T^{9} + 868583218 T^{10} + 917380028 T^{11} + 10779215329 T^{12} \))
$53$ (\( 1 + 4 T + 38 T^{2} + 212 T^{3} + 2809 T^{4} \))(\( 1 - 12 T + 123 T^{2} - 732 T^{3} + 6519 T^{4} - 33708 T^{5} + 148877 T^{6} \))(\( 1 + 2 T + 146 T^{2} + 322 T^{3} + 10283 T^{4} + 28788 T^{5} + 545108 T^{6} + 1525764 T^{7} + 28884947 T^{8} + 47938394 T^{9} + 1152010226 T^{10} + 836390986 T^{11} + 22164361129 T^{12} \))
$59$ (\( 1 + 10 T + 125 T^{2} + 590 T^{3} + 3481 T^{4} \))(\( 1 - 6 T + 5 T^{2} + 560 T^{3} + 295 T^{4} - 20886 T^{5} + 205379 T^{6} \))(\( 1 + 16 T + 389 T^{2} + 4106 T^{3} + 56583 T^{4} + 440906 T^{5} + 4375002 T^{6} + 26013454 T^{7} + 196965423 T^{8} + 843286174 T^{9} + 4713653429 T^{10} + 11438788784 T^{11} + 42180533641 T^{12} \))
$61$ (\( ( 1 + T )^{2} \))(\( ( 1 - T )^{3} \))(\( ( 1 + T )^{6} \))
$67$ (\( 1 - 6 T + 93 T^{2} - 402 T^{3} + 4489 T^{4} \))(\( 1 + 65 T^{2} - 496 T^{3} + 4355 T^{4} + 300763 T^{6} \))(\( 1 + 2 T + 161 T^{2} + 606 T^{3} + 16899 T^{4} + 67908 T^{5} + 1369430 T^{6} + 4549836 T^{7} + 75859611 T^{8} + 182262378 T^{9} + 3244330481 T^{10} + 2700250214 T^{11} + 90458382169 T^{12} \))
$71$ (\( ( 1 - 6 T + 71 T^{2} )^{2} \))(\( 1 - 14 T + 233 T^{2} - 1888 T^{3} + 16543 T^{4} - 70574 T^{5} + 357911 T^{6} \))(\( 1 + 18 T + 438 T^{2} + 5406 T^{3} + 76731 T^{4} + 709420 T^{5} + 7223660 T^{6} + 50368820 T^{7} + 386800971 T^{8} + 1934866866 T^{9} + 11130316278 T^{10} + 32476128318 T^{11} + 128100283921 T^{12} \))
$73$ (\( 1 + 10 T + 99 T^{2} + 730 T^{3} + 5329 T^{4} \))(\( 1 + 2 T + 71 T^{2} + 828 T^{3} + 5183 T^{4} + 10658 T^{5} + 389017 T^{6} \))(\( 1 - 30 T + 719 T^{2} - 11614 T^{3} + 160203 T^{4} - 1739636 T^{5} + 16506762 T^{6} - 126993428 T^{7} + 853721787 T^{8} - 4518043438 T^{9} + 20418335279 T^{10} - 62192147790 T^{11} + 151334226289 T^{12} \))
$79$ (\( 1 + 2 T + 157 T^{2} + 158 T^{3} + 6241 T^{4} \))(\( 1 + 12 T + 149 T^{2} + 1912 T^{3} + 11771 T^{4} + 74892 T^{5} + 493039 T^{6} \))(\( 1 - 6 T + 401 T^{2} - 1650 T^{3} + 68699 T^{4} - 203164 T^{5} + 6836870 T^{6} - 16049956 T^{7} + 428750459 T^{8} - 813514350 T^{9} + 15618982481 T^{10} - 18462338394 T^{11} + 243087455521 T^{12} \))
$83$ (\( 1 + 8 T + 174 T^{2} + 664 T^{3} + 6889 T^{4} \))(\( 1 + 8 T + 185 T^{2} + 1072 T^{3} + 15355 T^{4} + 55112 T^{5} + 571787 T^{6} \))(\( 1 + 12 T + 234 T^{2} + 2388 T^{3} + 34631 T^{4} + 291352 T^{5} + 3439916 T^{6} + 24182216 T^{7} + 238572959 T^{8} + 1365427356 T^{9} + 11105247114 T^{10} + 47268487716 T^{11} + 326940373369 T^{12} \))
$89$ (\( 1 + 16 T + 210 T^{2} + 1424 T^{3} + 7921 T^{4} \))(\( 1 + 4 T + 159 T^{2} + 660 T^{3} + 14151 T^{4} + 31684 T^{5} + 704969 T^{6} \))(\( 1 - 26 T + 550 T^{2} - 7986 T^{3} + 104323 T^{4} - 1107204 T^{5} + 11288476 T^{6} - 98541156 T^{7} + 826342483 T^{8} - 5629882434 T^{9} + 34508232550 T^{10} - 145185545674 T^{11} + 496981290961 T^{12} \))
$97$ (\( 1 + 12 T + 198 T^{2} + 1164 T^{3} + 9409 T^{4} \))(\( 1 - 18 T + 383 T^{2} - 3596 T^{3} + 37151 T^{4} - 169362 T^{5} + 912673 T^{6} \))(\( 1 - 16 T + 402 T^{2} - 5552 T^{3} + 76159 T^{4} - 885888 T^{5} + 9052124 T^{6} - 85931136 T^{7} + 716580031 T^{8} - 5067160496 T^{9} + 35588770962 T^{10} - 137397444112 T^{11} + 832972004929 T^{12} \))
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