Properties

Label 30.3.b
Level 30
Weight 3
Character orbit b
Rep. character \(\chi_{30}(29,\cdot)\)
Character field \(\Q\)
Dimension 4
Newform subspaces 1
Sturm bound 18
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 30 = 2 \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 30.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(18\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(30, [\chi])\).

Total New Old
Modular forms 16 4 12
Cusp forms 8 4 4
Eisenstein series 8 0 8

Trace form

\( 4q + 8q^{4} - 4q^{6} - 32q^{9} + O(q^{10}) \) \( 4q + 8q^{4} - 4q^{6} - 32q^{9} - 16q^{10} + 8q^{15} + 16q^{16} + 48q^{19} + 68q^{21} - 8q^{24} - 36q^{25} + 68q^{30} - 128q^{31} - 64q^{34} - 64q^{36} - 32q^{40} - 68q^{45} + 136q^{46} + 60q^{49} + 32q^{51} + 100q^{54} + 272q^{55} + 16q^{60} - 64q^{61} + 32q^{64} - 272q^{66} - 68q^{69} - 136q^{70} - 272q^{75} + 96q^{76} - 288q^{79} + 188q^{81} + 136q^{84} + 128q^{85} + 128q^{90} - 200q^{94} - 16q^{96} + 272q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(30, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
30.3.b.a \(4\) \(0.817\) \(\Q(\sqrt{2}, \sqrt{-17})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{2})q^{3}+2q^{4}+(-2\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(30, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(30, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( ( 1 - 2 T^{2} )^{2} \)
$3$ \( 1 + 16 T^{2} + 81 T^{4} \)
$5$ \( 1 + 18 T^{2} + 625 T^{4} \)
$7$ \( ( 1 - 64 T^{2} + 2401 T^{4} )^{2} \)
$11$ \( ( 1 + 30 T^{2} + 14641 T^{4} )^{2} \)
$13$ \( ( 1 - 13 T )^{4}( 1 + 13 T )^{4} \)
$17$ \( ( 1 + 450 T^{2} + 83521 T^{4} )^{2} \)
$19$ \( ( 1 - 12 T + 361 T^{2} )^{4} \)
$23$ \( ( 1 + 480 T^{2} + 279841 T^{4} )^{2} \)
$29$ \( ( 1 - 29 T )^{4}( 1 + 29 T )^{4} \)
$31$ \( ( 1 + 32 T + 961 T^{2} )^{4} \)
$37$ \( ( 1 - 2194 T^{2} + 1874161 T^{4} )^{2} \)
$41$ \( ( 1 - 30 T^{2} + 2825761 T^{4} )^{2} \)
$43$ \( ( 1 - 2032 T^{2} + 3418801 T^{4} )^{2} \)
$47$ \( ( 1 + 3168 T^{2} + 4879681 T^{4} )^{2} \)
$53$ \( ( 1 + 1010 T^{2} + 7890481 T^{4} )^{2} \)
$59$ \( ( 1 - 6690 T^{2} + 12117361 T^{4} )^{2} \)
$61$ \( ( 1 + 16 T + 3721 T^{2} )^{4} \)
$67$ \( ( 1 - 8944 T^{2} + 20151121 T^{4} )^{2} \)
$71$ \( ( 1 - 71 T )^{4}( 1 + 71 T )^{4} \)
$73$ \( ( 1 + 2942 T^{2} + 28398241 T^{4} )^{2} \)
$79$ \( ( 1 + 72 T + 6241 T^{2} )^{4} \)
$83$ \( ( 1 + 11856 T^{2} + 47458321 T^{4} )^{2} \)
$89$ \( ( 1 - 11490 T^{2} + 62742241 T^{4} )^{2} \)
$97$ \( ( 1 + 7838 T^{2} + 88529281 T^{4} )^{2} \)
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