Properties

Label 12.5.c
Level 12
Weight 5
Character orbit c
Rep. character \(\chi_{12}(5,\cdot)\)
Character field \(\Q\)
Dimension 1
Newform subspaces 1
Sturm bound 10
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 12.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(10\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(12, [\chi])\).

Total New Old
Modular forms 11 1 10
Cusp forms 5 1 4
Eisenstein series 6 0 6

Trace form

\( q + 9q^{3} - 94q^{7} + 81q^{9} + O(q^{10}) \) \( q + 9q^{3} - 94q^{7} + 81q^{9} + 146q^{13} - 46q^{19} - 846q^{21} + 625q^{25} + 729q^{27} + 194q^{31} - 2062q^{37} + 1314q^{39} - 3214q^{43} + 6435q^{49} - 414q^{57} - 1966q^{61} - 7614q^{63} + 5906q^{67} - 8542q^{73} + 5625q^{75} + 7682q^{79} + 6561q^{81} - 13724q^{91} + 1746q^{93} - 18814q^{97} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(12, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
12.5.c.a \(1\) \(1.240\) \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(9\) \(0\) \(-94\) \(q+9q^{3}-94q^{7}+3^{4}q^{9}+146q^{13}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(12, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(12, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ \( 1 - 9 T \)
$5$ \( ( 1 - 25 T )( 1 + 25 T ) \)
$7$ \( 1 + 94 T + 2401 T^{2} \)
$11$ \( ( 1 - 121 T )( 1 + 121 T ) \)
$13$ \( 1 - 146 T + 28561 T^{2} \)
$17$ \( ( 1 - 289 T )( 1 + 289 T ) \)
$19$ \( 1 + 46 T + 130321 T^{2} \)
$23$ \( ( 1 - 529 T )( 1 + 529 T ) \)
$29$ \( ( 1 - 841 T )( 1 + 841 T ) \)
$31$ \( 1 - 194 T + 923521 T^{2} \)
$37$ \( 1 + 2062 T + 1874161 T^{2} \)
$41$ \( ( 1 - 1681 T )( 1 + 1681 T ) \)
$43$ \( 1 + 3214 T + 3418801 T^{2} \)
$47$ \( ( 1 - 2209 T )( 1 + 2209 T ) \)
$53$ \( ( 1 - 2809 T )( 1 + 2809 T ) \)
$59$ \( ( 1 - 3481 T )( 1 + 3481 T ) \)
$61$ \( 1 + 1966 T + 13845841 T^{2} \)
$67$ \( 1 - 5906 T + 20151121 T^{2} \)
$71$ \( ( 1 - 5041 T )( 1 + 5041 T ) \)
$73$ \( 1 + 8542 T + 28398241 T^{2} \)
$79$ \( 1 - 7682 T + 38950081 T^{2} \)
$83$ \( ( 1 - 6889 T )( 1 + 6889 T ) \)
$89$ \( ( 1 - 7921 T )( 1 + 7921 T ) \)
$97$ \( 1 + 18814 T + 88529281 T^{2} \)
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