Properties

Label 1512.2.k
Level 1512
Weight 2
Character orbit k
Rep. character \(\chi_{1512}(377,\cdot)\)
Character field \(\Q\)
Dimension 32
Newform subspaces 2
Sturm bound 576
Trace bound 25

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1512.k (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(576\)
Trace bound: \(25\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1512, [\chi])\).

Total New Old
Modular forms 312 32 280
Cusp forms 264 32 232
Eisenstein series 48 0 48

Trace form

\( 32q - 4q^{7} + O(q^{10}) \) \( 32q - 4q^{7} + 24q^{25} - 16q^{37} + 28q^{43} + 4q^{49} + 16q^{67} - 4q^{79} + 32q^{85} + 54q^{91} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1512, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1512.2.k.a \(16\) \(12.073\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-2\) \(q-\beta _{9}q^{5}-\beta _{1}q^{7}-\beta _{10}q^{11}-\beta _{5}q^{13}+\cdots\)
1512.2.k.b \(16\) \(12.073\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-2\) \(q+\beta _{1}q^{5}-\beta _{12}q^{7}+\beta _{10}q^{11}+(\beta _{4}+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1512, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1512, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( \))(\( \))
$3$ (\( \))(\( \))
$5$ (\( ( 1 + 23 T^{2} + 273 T^{4} + 2194 T^{6} + 12806 T^{8} + 54850 T^{10} + 170625 T^{12} + 359375 T^{14} + 390625 T^{16} )^{2} \))(\( ( 1 + 11 T^{2} + 45 T^{4} + 34 T^{6} - 214 T^{8} + 850 T^{10} + 28125 T^{12} + 171875 T^{14} + 390625 T^{16} )^{2} \))
$7$ (\( ( 1 + T + 5 T^{3} - 34 T^{4} + 35 T^{5} + 343 T^{7} + 2401 T^{8} )^{2} \))(\( ( 1 + T - 7 T^{3} + 14 T^{4} - 49 T^{5} + 343 T^{7} + 2401 T^{8} )^{2} \))
$11$ (\( ( 1 - 37 T^{2} + 801 T^{4} - 12446 T^{6} + 149966 T^{8} - 1505966 T^{10} + 11727441 T^{12} - 65547757 T^{14} + 214358881 T^{16} )^{2} \))(\( ( 1 - 55 T^{2} + 1590 T^{4} - 29597 T^{6} + 386186 T^{8} - 3581237 T^{10} + 23279190 T^{12} - 97435855 T^{14} + 214358881 T^{16} )^{2} \))
$13$ (\( ( 1 - 49 T^{2} + 1398 T^{4} - 28055 T^{6} + 418226 T^{8} - 4741295 T^{10} + 39928278 T^{12} - 236513641 T^{14} + 815730721 T^{16} )^{2} \))(\( ( 1 - 49 T^{2} + 1362 T^{4} - 26411 T^{6} + 392258 T^{8} - 4463459 T^{10} + 38900082 T^{12} - 236513641 T^{14} + 815730721 T^{16} )^{2} \))
$17$ (\( ( 1 + 72 T^{2} + 2652 T^{4} + 65784 T^{6} + 1248326 T^{8} + 19011576 T^{10} + 221497692 T^{12} + 1737904968 T^{14} + 6975757441 T^{16} )^{2} \))(\( ( 1 + 87 T^{2} + 3537 T^{4} + 92514 T^{6} + 1788926 T^{8} + 26736546 T^{10} + 295413777 T^{12} + 2099968503 T^{14} + 6975757441 T^{16} )^{2} \))
$19$ (\( ( 1 - 100 T^{2} + 4914 T^{4} - 156608 T^{6} + 3515195 T^{8} - 56535488 T^{10} + 640397394 T^{12} - 4704588100 T^{14} + 16983563041 T^{16} )^{2} \))(\( ( 1 - 112 T^{2} + 5952 T^{4} - 197456 T^{6} + 4482014 T^{8} - 71281616 T^{10} + 775670592 T^{12} - 5269138672 T^{14} + 16983563041 T^{16} )^{2} \))
$23$ (\( ( 1 - 21 T^{2} + 697 T^{4} - 11718 T^{6} + 312438 T^{8} - 6198822 T^{10} + 195049177 T^{12} - 3108753669 T^{14} + 78310985281 T^{16} )^{2} \))(\( ( 1 - 99 T^{2} + 5182 T^{4} - 187533 T^{6} + 5005890 T^{8} - 99204957 T^{10} + 1450136062 T^{12} - 14655553011 T^{14} + 78310985281 T^{16} )^{2} \))
$29$ (\( ( 1 - 172 T^{2} + 14052 T^{4} - 714740 T^{6} + 24798806 T^{8} - 601096340 T^{10} + 9938712612 T^{12} - 102309611212 T^{14} + 500246412961 T^{16} )^{2} \))(\( ( 1 - 103 T^{2} + 5226 T^{4} - 168029 T^{6} + 4755218 T^{8} - 141312389 T^{10} + 3696250506 T^{12} - 61266802063 T^{14} + 500246412961 T^{16} )^{2} \))
$31$ (\( ( 1 - 187 T^{2} + 16353 T^{4} - 883634 T^{6} + 32653478 T^{8} - 849172274 T^{10} + 15102338913 T^{12} - 165963188347 T^{14} + 852891037441 T^{16} )^{2} \))(\( ( 1 - 94 T^{2} + 5349 T^{4} - 230570 T^{6} + 7832744 T^{8} - 221577770 T^{10} + 4939913829 T^{12} - 83425346014 T^{14} + 852891037441 T^{16} )^{2} \))
$37$ (\( ( 1 + 2 T + 52 T^{2} - 100 T^{3} + 949 T^{4} - 3700 T^{5} + 71188 T^{6} + 101306 T^{7} + 1874161 T^{8} )^{4} \))(\( ( 1 + 2 T + 49 T^{2} + 410 T^{3} + 1084 T^{4} + 15170 T^{5} + 67081 T^{6} + 101306 T^{7} + 1874161 T^{8} )^{4} \))
$41$ (\( ( 1 + 135 T^{2} + 11289 T^{4} + 646218 T^{6} + 29821310 T^{8} + 1086292458 T^{10} + 31900015929 T^{12} + 641264072535 T^{14} + 7984925229121 T^{16} )^{2} \))(\( ( 1 + 102 T^{2} + 10017 T^{4} + 548706 T^{6} + 28065644 T^{8} + 922374786 T^{10} + 28305647937 T^{12} + 484510632582 T^{14} + 7984925229121 T^{16} )^{2} \))
$43$ (\( ( 1 - 2 T + 40 T^{2} + 118 T^{3} - 194 T^{4} + 5074 T^{5} + 73960 T^{6} - 159014 T^{7} + 3418801 T^{8} )^{4} \))(\( ( 1 - 5 T + 109 T^{2} - 248 T^{3} + 5122 T^{4} - 10664 T^{5} + 201541 T^{6} - 397535 T^{7} + 3418801 T^{8} )^{4} \))
$47$ (\( ( 1 + 20 T^{2} + 4068 T^{4} + 4972 T^{6} + 7535798 T^{8} + 10983148 T^{10} + 19850542308 T^{12} + 215584306580 T^{14} + 23811286661761 T^{16} )^{2} \))(\( ( 1 + 278 T^{2} + 35193 T^{4} + 2749546 T^{6} + 150940940 T^{8} + 6073747114 T^{10} + 171730613433 T^{12} + 2996621861462 T^{14} + 23811286661761 T^{16} )^{2} \))
$53$ (\( ( 1 - 184 T^{2} + 17436 T^{4} - 1193288 T^{6} + 68587430 T^{8} - 3351945992 T^{10} + 137578426716 T^{12} - 4078242447736 T^{14} + 62259690411361 T^{16} )^{2} \))(\( ( 1 - 142 T^{2} + 13833 T^{4} - 1028534 T^{6} + 58011620 T^{8} - 2889152006 T^{10} + 109149023673 T^{12} - 3147339280318 T^{14} + 62259690411361 T^{16} )^{2} \))
$59$ (\( ( 1 + 148 T^{2} + 10276 T^{4} + 457612 T^{6} + 23078422 T^{8} + 1592947372 T^{10} + 124518001636 T^{12} + 6242718978868 T^{14} + 146830437604321 T^{16} )^{2} \))(\( ( 1 + 283 T^{2} + 41785 T^{4} + 4061626 T^{6} + 280646974 T^{8} + 14138520106 T^{10} + 506323929385 T^{12} + 11937091020403 T^{14} + 146830437604321 T^{16} )^{2} \))
$61$ (\( ( 1 - 317 T^{2} + 50098 T^{4} - 5135915 T^{6} + 370298362 T^{8} - 19110739715 T^{10} + 693648942418 T^{12} - 16331958672437 T^{14} + 191707312997281 T^{16} )^{2} \))(\( ( 1 - 236 T^{2} + 32440 T^{4} - 3088964 T^{6} + 216205582 T^{8} - 11494035044 T^{10} + 449159082040 T^{12} - 12158808349196 T^{14} + 191707312997281 T^{16} )^{2} \))
$67$ (\( ( 1 + 7 T + 114 T^{2} + 35 T^{3} + 3554 T^{4} + 2345 T^{5} + 511746 T^{6} + 2105341 T^{7} + 20151121 T^{8} )^{4} \))(\( ( 1 - 11 T + 198 T^{2} - 2071 T^{3} + 17498 T^{4} - 138757 T^{5} + 888822 T^{6} - 3308393 T^{7} + 20151121 T^{8} )^{4} \))
$71$ (\( ( 1 - 341 T^{2} + 63193 T^{4} - 7537622 T^{6} + 634982182 T^{8} - 37997152502 T^{10} + 1605840357433 T^{12} - 43682196817061 T^{14} + 645753531245761 T^{16} )^{2} \))(\( ( 1 - 167 T^{2} + 18034 T^{4} - 1223801 T^{6} + 87222970 T^{8} - 6169180841 T^{10} + 458274255154 T^{12} - 21392747414807 T^{14} + 645753531245761 T^{16} )^{2} \))
$73$ (\( ( 1 - 321 T^{2} + 57726 T^{4} - 6821535 T^{6} + 583944098 T^{8} - 36351960015 T^{10} + 1639316859966 T^{12} - 48578286638769 T^{14} + 806460091894081 T^{16} )^{2} \))(\( ( 1 - 117 T^{2} + 15114 T^{4} - 1400907 T^{6} + 111599882 T^{8} - 7465433403 T^{10} + 429211014474 T^{12} - 17706104475813 T^{14} + 806460091894081 T^{16} )^{2} \))
$79$ (\( ( 1 + 11 T + 246 T^{2} + 2515 T^{3} + 26570 T^{4} + 198685 T^{5} + 1535286 T^{6} + 5423429 T^{7} + 38950081 T^{8} )^{4} \))(\( ( 1 - 10 T + 261 T^{2} - 1850 T^{3} + 28244 T^{4} - 146150 T^{5} + 1628901 T^{6} - 4930390 T^{7} + 38950081 T^{8} )^{4} \))
$83$ (\( ( 1 + 132 T^{2} + 12996 T^{4} + 1459932 T^{6} + 170705174 T^{8} + 10057471548 T^{10} + 616768339716 T^{12} + 43156129284708 T^{14} + 2252292232139041 T^{16} )^{2} \))(\( ( 1 + 339 T^{2} + 56745 T^{4} + 6361962 T^{6} + 567506462 T^{8} + 43827556218 T^{10} + 2693022425145 T^{12} + 110832786572091 T^{14} + 2252292232139041 T^{16} )^{2} \))
$89$ (\( ( 1 + 351 T^{2} + 57993 T^{4} + 6040074 T^{6} + 534549758 T^{8} + 47843426154 T^{10} + 3638610782313 T^{12} + 174440433127311 T^{14} + 3936588805702081 T^{16} )^{2} \))(\( ( 1 + 321 T^{2} + 55134 T^{4} + 6909375 T^{6} + 691071074 T^{8} + 54729159375 T^{10} + 3459230715294 T^{12} + 159530994398481 T^{14} + 3936588805702081 T^{16} )^{2} \))
$97$ (\( ( 1 - 285 T^{2} + 64986 T^{4} - 9080499 T^{6} + 1059084650 T^{8} - 85438415091 T^{10} + 5753163855066 T^{12} - 237397021404765 T^{14} + 7837433594376961 T^{16} )^{2} \))(\( ( 1 - 537 T^{2} + 140634 T^{4} - 23455755 T^{6} + 2707648082 T^{8} - 220695198795 T^{10} + 12450226904154 T^{12} - 447305966646873 T^{14} + 7837433594376961 T^{16} )^{2} \))
show more
show less