Properties

Label 456.2.g
Level $456$
Weight $2$
Character orbit 456.g
Rep. character $\chi_{456}(229,\cdot)$
Character field $\Q$
Dimension $36$
Newform subspaces $2$
Sturm bound $160$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 456.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(160\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(456, [\chi])\).

Total New Old
Modular forms 84 36 48
Cusp forms 76 36 40
Eisenstein series 8 0 8

Trace form

\( 36q + 4q^{2} - 4q^{4} + 8q^{7} + 4q^{8} - 36q^{9} + O(q^{10}) \) \( 36q + 4q^{2} - 4q^{4} + 8q^{7} + 4q^{8} - 36q^{9} + 8q^{10} - 8q^{12} - 20q^{14} + 20q^{16} + 8q^{17} - 4q^{18} - 16q^{20} - 20q^{22} - 16q^{23} + 12q^{24} - 44q^{25} + 16q^{26} + 8q^{28} + 8q^{30} + 4q^{32} + 12q^{34} + 4q^{36} + 16q^{39} - 28q^{40} - 8q^{41} - 8q^{42} + 8q^{44} + 52q^{46} - 16q^{48} + 36q^{49} + 8q^{50} - 36q^{52} + 24q^{56} - 16q^{58} + 20q^{60} - 48q^{62} - 8q^{63} - 4q^{64} - 32q^{65} + 8q^{66} + 32q^{68} + 28q^{70} - 48q^{71} - 4q^{72} + 40q^{73} - 56q^{74} - 12q^{78} + 16q^{79} - 8q^{80} + 36q^{81} + 24q^{82} - 8q^{84} - 20q^{86} + 24q^{87} + 40q^{89} - 8q^{90} - 48q^{92} + 8q^{94} - 20q^{96} - 8q^{97} + 8q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(456, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
456.2.g.a \(18\) \(3.641\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(2\) \(0\) \(0\) \(-12\) \(q+\beta _{14}q^{2}-\beta _{3}q^{3}-\beta _{2}q^{4}+\beta _{13}q^{5}+\cdots\)
456.2.g.b \(18\) \(3.641\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(2\) \(0\) \(0\) \(20\) \(q+\beta _{9}q^{2}+\beta _{4}q^{3}+\beta _{2}q^{4}-\beta _{5}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(456, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(456, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 2}\)