Properties

Label 154.2.c
Level 154
Weight 2
Character orbit c
Rep. character \(\chi_{154}(153,\cdot)\)
Character field \(\Q\)
Dimension 8
Newform subspaces 1
Sturm bound 48
Trace bound 0

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Defining parameters

Level: \( N \) = \( 154 = 2 \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 154.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 77 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(48\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(154, [\chi])\).

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

Trace form

\( 8q - 8q^{4} - 16q^{9} + O(q^{10}) \) \( 8q - 8q^{4} - 16q^{9} + 4q^{11} + 8q^{14} - 16q^{15} + 8q^{16} - 4q^{22} + 32q^{23} + 16q^{36} - 8q^{37} - 24q^{42} - 4q^{44} + 40q^{49} - 56q^{53} - 8q^{56} - 24q^{58} + 16q^{60} - 8q^{64} - 24q^{67} + 24q^{70} + 16q^{71} + 4q^{77} + 40q^{78} + 80q^{81} + 16q^{86} + 4q^{88} - 24q^{91} - 32q^{92} + 8q^{93} - 92q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(154, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
154.2.c.a \(8\) \(1.230\) 8.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{2}q^{3}-q^{4}+\beta _{6}q^{5}-\beta _{3}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(154, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(154, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( ( 1 + T^{2} )^{4} \)
$3$ \( ( 1 - 2 T^{2} - 2 T^{4} - 18 T^{6} + 81 T^{8} )^{2} \)
$5$ \( ( 1 - 10 T^{2} + 54 T^{4} - 250 T^{6} + 625 T^{8} )^{2} \)
$7$ \( ( 1 - 10 T^{2} + 49 T^{4} )^{2} \)
$11$ \( ( 1 - 2 T + 2 T^{2} - 22 T^{3} + 121 T^{4} )^{2} \)
$13$ \( ( 1 + 42 T^{2} + 758 T^{4} + 7098 T^{6} + 28561 T^{8} )^{2} \)
$17$ \( ( 1 + 20 T^{2} + 289 T^{4} )^{4} \)
$19$ \( ( 1 + 42 T^{2} + 974 T^{4} + 15162 T^{6} + 130321 T^{8} )^{2} \)
$23$ \( ( 1 - 4 T + 23 T^{2} )^{8} \)
$29$ \( ( 1 - 56 T^{2} + 1710 T^{4} - 47096 T^{6} + 707281 T^{8} )^{2} \)
$31$ \( ( 1 - 48 T^{2} + 1154 T^{4} - 46128 T^{6} + 923521 T^{8} )^{2} \)
$37$ \( ( 1 + 2 T + 54 T^{2} + 74 T^{3} + 1369 T^{4} )^{4} \)
$41$ \( ( 1 + 40 T^{2} + 2418 T^{4} + 67240 T^{6} + 2825761 T^{8} )^{2} \)
$43$ \( ( 1 + 4 T^{2} + 2358 T^{4} + 7396 T^{6} + 3418801 T^{8} )^{2} \)
$47$ \( ( 1 - 64 T^{2} + 4098 T^{4} - 141376 T^{6} + 4879681 T^{8} )^{2} \)
$53$ \( ( 1 + 14 T + 134 T^{2} + 742 T^{3} + 2809 T^{4} )^{4} \)
$59$ \( ( 1 - 226 T^{2} + 19710 T^{4} - 786706 T^{6} + 12117361 T^{8} )^{2} \)
$61$ \( ( 1 + 154 T^{2} + 11670 T^{4} + 573034 T^{6} + 13845841 T^{8} )^{2} \)
$67$ \( ( 1 + 6 T + 122 T^{2} + 402 T^{3} + 4489 T^{4} )^{4} \)
$71$ \( ( 1 - 2 T + 71 T^{2} )^{8} \)
$73$ \( ( 1 - 8 T^{2} - 1422 T^{4} - 42632 T^{6} + 28398241 T^{8} )^{2} \)
$79$ \( ( 1 - 142 T^{2} + 6241 T^{4} )^{4} \)
$83$ \( ( 1 + 82 T^{2} + 13758 T^{4} + 564898 T^{6} + 47458321 T^{8} )^{2} \)
$89$ \( ( 1 - 82 T^{2} + 7921 T^{4} )^{4} \)
$97$ \( ( 1 - 60 T^{2} + 11318 T^{4} - 564540 T^{6} + 88529281 T^{8} )^{2} \)
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