Properties

Label 308.2.c
Level 308
Weight 2
Character orbit c
Rep. character \(\chi_{308}(153,\cdot)\)
Character field \(\Q\)
Dimension 8
Newform subspaces 2
Sturm bound 96
Trace bound 9

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Defining parameters

Level: \( N \) = \( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 308.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 77 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(96\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(308, [\chi])\).

Total New Old
Modular forms 54 8 46
Cusp forms 42 8 34
Eisenstein series 12 0 12

Trace form

\( 8q - 4q^{9} + O(q^{10}) \) \( 8q - 4q^{9} + 4q^{11} - 4q^{15} - 4q^{23} - 12q^{25} + 28q^{37} - 20q^{49} + 16q^{53} - 12q^{67} + 28q^{71} - 8q^{77} - 64q^{81} + 24q^{91} - 28q^{93} + 16q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(308, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
308.2.c.a \(4\) \(2.459\) \(\Q(\sqrt{2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{3}q^{3}-\beta _{3}q^{5}+(\beta _{1}-\beta _{2})q^{7}-2q^{9}+\cdots\)
308.2.c.b \(4\) \(2.459\) \(\Q(\sqrt{-2}, \sqrt{-7})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{3}-2\beta _{2}q^{5}-\beta _{3}q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(308, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(308, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( \))(\( \))
$3$ (\( ( 1 - T^{2} + 9 T^{4} )^{2} \))(\( ( 1 - 4 T^{2} + 9 T^{4} )^{2} \))
$5$ (\( ( 1 - 5 T^{2} + 25 T^{4} )^{2} \))(\( ( 1 - 2 T^{2} + 25 T^{4} )^{2} \))
$7$ (\( 1 - 4 T^{2} + 49 T^{4} \))(\( ( 1 + 7 T^{2} )^{2} \))
$11$ (\( ( 1 + 2 T + 11 T^{2} )^{2} \))(\( ( 1 - 4 T + 11 T^{2} )^{2} \))
$13$ (\( ( 1 + 18 T^{2} + 169 T^{4} )^{2} \))(\( ( 1 + 12 T^{2} + 169 T^{4} )^{2} \))
$17$ (\( ( 1 + 2 T^{2} + 289 T^{4} )^{2} \))(\( ( 1 + 20 T^{2} + 289 T^{4} )^{2} \))
$19$ (\( ( 1 + 36 T^{2} + 361 T^{4} )^{2} \))(\( ( 1 - 18 T^{2} + 361 T^{4} )^{2} \))
$23$ (\( ( 1 + 5 T + 23 T^{2} )^{4} \))(\( ( 1 - 4 T + 23 T^{2} )^{4} \))
$29$ (\( ( 1 + 32 T^{2} + 841 T^{4} )^{2} \))(\( ( 1 - 29 T^{2} )^{4} \))
$31$ (\( ( 1 - 57 T^{2} + 961 T^{4} )^{2} \))(\( ( 1 - 60 T^{2} + 961 T^{4} )^{2} \))
$37$ (\( ( 1 - 11 T + 37 T^{2} )^{4} \))(\( ( 1 + 4 T + 37 T^{2} )^{4} \))
$41$ (\( ( 1 - 16 T^{2} + 1681 T^{4} )^{2} \))(\( ( 1 + 68 T^{2} + 1681 T^{4} )^{2} \))
$43$ (\( ( 1 - 76 T^{2} + 1849 T^{4} )^{2} \))(\( ( 1 + 26 T^{2} + 1849 T^{4} )^{2} \))
$47$ (\( ( 1 - 74 T^{2} + 2209 T^{4} )^{2} \))(\( ( 1 + 4 T^{2} + 2209 T^{4} )^{2} \))
$53$ (\( ( 1 - 8 T + 53 T^{2} )^{4} \))(\( ( 1 + 4 T + 53 T^{2} )^{4} \))
$59$ (\( ( 1 - 113 T^{2} + 3481 T^{4} )^{2} \))(\( ( 1 - 116 T^{2} + 3481 T^{4} )^{2} \))
$61$ (\( ( 1 + 104 T^{2} + 3721 T^{4} )^{2} \))(\( ( 1 - 4 T^{2} + 3721 T^{4} )^{2} \))
$67$ (\( ( 1 - 9 T + 67 T^{2} )^{4} \))(\( ( 1 + 12 T + 67 T^{2} )^{4} \))
$71$ (\( ( 1 + T + 71 T^{2} )^{4} \))(\( ( 1 - 8 T + 71 T^{2} )^{4} \))
$73$ (\( ( 1 + 128 T^{2} + 5329 T^{4} )^{2} \))(\( ( 1 + 20 T^{2} + 5329 T^{4} )^{2} \))
$79$ (\( ( 1 - 118 T^{2} + 6241 T^{4} )^{2} \))(\( ( 1 - 46 T^{2} + 6241 T^{4} )^{2} \))
$83$ (\( ( 1 + 164 T^{2} + 6889 T^{4} )^{2} \))(\( ( 1 + 110 T^{2} + 6889 T^{4} )^{2} \))
$89$ (\( ( 1 - 133 T^{2} + 7921 T^{4} )^{2} \))(\( ( 1 + 110 T^{2} + 7921 T^{4} )^{2} \))
$97$ (\( ( 1 + 51 T^{2} + 9409 T^{4} )^{2} \))(\( ( 1 - 162 T^{2} + 9409 T^{4} )^{2} \))
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