Properties

Label 231.2.c
Level 231
Weight 2
Character orbit c
Rep. character \(\chi_{231}(76,\cdot)\)
Character field \(\Q\)
Dimension 16
Newform subspaces 1
Sturm bound 64
Trace bound 0

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Defining parameters

Level: \( N \) = \( 231 = 3 \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 231.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 77 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(64\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(231, [\chi])\).

Total New Old
Modular forms 36 16 20
Cusp forms 28 16 12
Eisenstein series 8 0 8

Trace form

\( 16q - 12q^{4} - 16q^{9} + O(q^{10}) \) \( 16q - 12q^{4} - 16q^{9} + 16q^{11} + 8q^{14} - 8q^{15} - 4q^{16} - 20q^{22} + 24q^{23} - 24q^{25} + 12q^{36} + 8q^{37} + 12q^{42} - 32q^{44} + 24q^{53} - 40q^{56} - 12q^{58} + 36q^{60} + 88q^{64} - 32q^{67} + 36q^{70} - 48q^{71} + 12q^{78} + 16q^{81} + 32q^{86} + 16q^{91} - 128q^{92} - 40q^{93} - 16q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(231, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
231.2.c.a \(16\) \(1.845\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{6}q^{2}-\beta _{8}q^{3}+(-1+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(231, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(231, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( ( 1 - 5 T^{2} + 16 T^{4} - 45 T^{6} + 101 T^{8} - 180 T^{10} + 256 T^{12} - 320 T^{14} + 256 T^{16} )^{2} \)
$3$ \( ( 1 + T^{2} )^{8} \)
$5$ \( ( 1 - 14 T^{2} + 121 T^{4} - 774 T^{6} + 4196 T^{8} - 19350 T^{10} + 75625 T^{12} - 218750 T^{14} + 390625 T^{16} )^{2} \)
$7$ \( 1 - 4 T^{4} - 314 T^{8} - 9604 T^{12} + 5764801 T^{16} \)
$11$ \( ( 1 - 4 T + 6 T^{2} - 44 T^{3} + 121 T^{4} )^{4} \)
$13$ \( ( 1 + 70 T^{2} + 2381 T^{4} + 51950 T^{6} + 796636 T^{8} + 8779550 T^{10} + 68003741 T^{12} + 337876630 T^{14} + 815730721 T^{16} )^{2} \)
$17$ \( ( 1 + 20 T^{2} + 1076 T^{4} + 16300 T^{6} + 457366 T^{8} + 4710700 T^{10} + 89868596 T^{12} + 482751380 T^{14} + 6975757441 T^{16} )^{2} \)
$19$ \( ( 1 + 102 T^{2} + 5093 T^{4} + 161814 T^{6} + 3616780 T^{8} + 58414854 T^{10} + 663724853 T^{12} + 4798679862 T^{14} + 16983563041 T^{16} )^{2} \)
$23$ \( ( 1 - 6 T + 48 T^{2} - 270 T^{3} + 1086 T^{4} - 6210 T^{5} + 25392 T^{6} - 73002 T^{7} + 279841 T^{8} )^{4} \)
$29$ \( ( 1 - 158 T^{2} + 12293 T^{4} - 609286 T^{6} + 20954380 T^{8} - 512409526 T^{10} + 8694605333 T^{12} - 93982084718 T^{14} + 500246412961 T^{16} )^{2} \)
$31$ \( ( 1 - 108 T^{2} + 7028 T^{4} - 324436 T^{6} + 11297430 T^{8} - 311782996 T^{10} + 6490505588 T^{12} - 95850397548 T^{14} + 852891037441 T^{16} )^{2} \)
$37$ \( ( 1 - 2 T + 97 T^{2} - 250 T^{3} + 4636 T^{4} - 9250 T^{5} + 132793 T^{6} - 101306 T^{7} + 1874161 T^{8} )^{4} \)
$41$ \( ( 1 + 192 T^{2} + 16508 T^{4} + 888384 T^{6} + 38165830 T^{8} + 1493373504 T^{10} + 46647662588 T^{12} + 912020014272 T^{14} + 7984925229121 T^{16} )^{2} \)
$43$ \( ( 1 - 140 T^{2} + 13796 T^{4} - 867860 T^{6} + 43988886 T^{8} - 1604673140 T^{10} + 47165778596 T^{12} - 884990826860 T^{14} + 11688200277601 T^{16} )^{2} \)
$47$ \( ( 1 - 230 T^{2} + 28521 T^{4} - 2266390 T^{6} + 126631796 T^{8} - 5006455510 T^{10} + 139173381801 T^{12} - 2479219525670 T^{14} + 23811286661761 T^{16} )^{2} \)
$53$ \( ( 1 - 6 T + 188 T^{2} - 850 T^{3} + 14486 T^{4} - 45050 T^{5} + 528092 T^{6} - 893262 T^{7} + 7890481 T^{8} )^{4} \)
$59$ \( ( 1 - 278 T^{2} + 40073 T^{4} - 3829126 T^{6} + 263019940 T^{8} - 13329187606 T^{10} + 485579007353 T^{12} - 11726188352198 T^{14} + 146830437604321 T^{16} )^{2} \)
$61$ \( ( 1 + 312 T^{2} + 48988 T^{4} + 5009224 T^{6} + 360566630 T^{8} + 18639322504 T^{10} + 678280058908 T^{12} + 16074356800632 T^{14} + 191707312997281 T^{16} )^{2} \)
$67$ \( ( 1 + 8 T + 207 T^{2} + 1600 T^{3} + 18936 T^{4} + 107200 T^{5} + 929223 T^{6} + 2406104 T^{7} + 20151121 T^{8} )^{4} \)
$71$ \( ( 1 + 12 T + 248 T^{2} + 1804 T^{3} + 23150 T^{4} + 128084 T^{5} + 1250168 T^{6} + 4294932 T^{7} + 25411681 T^{8} )^{4} \)
$73$ \( ( 1 - 10 T^{2} + 18381 T^{4} - 178370 T^{6} + 140146796 T^{8} - 950533730 T^{10} + 521988067821 T^{12} - 1513342262890 T^{14} + 806460091894081 T^{16} )^{2} \)
$79$ \( ( 1 - 168 T^{2} + 16988 T^{4} - 1063576 T^{6} + 82499910 T^{8} - 6637777816 T^{10} + 661683976028 T^{12} - 40838692527528 T^{14} + 1517108809906561 T^{16} )^{2} \)
$83$ \( ( 1 + 180 T^{2} + 21956 T^{4} + 2097260 T^{6} + 156627606 T^{8} + 14448024140 T^{10} + 1041994895876 T^{12} + 58849267206420 T^{14} + 2252292232139041 T^{16} )^{2} \)
$89$ \( ( 1 - 528 T^{2} + 133148 T^{4} - 20911856 T^{6} + 2232438150 T^{8} - 165642811376 T^{10} + 8354003904668 T^{12} - 262406121627408 T^{14} + 3936588805702081 T^{16} )^{2} \)
$97$ \( ( 1 - 60 T^{2} + 15076 T^{4} - 1727620 T^{6} + 110798006 T^{8} - 16255176580 T^{10} + 1334667440356 T^{12} - 49978320295740 T^{14} + 7837433594376961 T^{16} )^{2} \)
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