Properties

Label 456.2.bu
Level $456$
Weight $2$
Character orbit 456.bu
Rep. character $\chi_{456}(35,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $456$
Newform subspaces $3$
Sturm bound $160$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 456.bu (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 456 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 3 \)
Sturm bound: \(160\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

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

Total New Old
Modular forms 504 504 0
Cusp forms 456 456 0
Eisenstein series 48 48 0

Trace form

\( 456q - 12q^{3} - 6q^{4} - 6q^{6} - 12q^{9} + O(q^{10}) \) \( 456q - 12q^{3} - 6q^{4} - 6q^{6} - 12q^{9} - 18q^{10} - 3q^{12} - 6q^{16} - 12q^{18} - 24q^{19} - 24q^{22} + 6q^{24} - 24q^{25} - 6q^{27} - 36q^{28} - 48q^{30} - 30q^{33} - 54q^{34} + 54q^{36} + 18q^{40} - 51q^{42} - 24q^{43} - 6q^{46} + 69q^{48} + 144q^{49} - 12q^{51} + 12q^{52} + 21q^{54} - 12q^{57} - 96q^{58} + 48q^{60} - 48q^{64} - 54q^{66} - 24q^{67} - 162q^{70} + 12q^{72} - 48q^{73} - 192q^{75} - 132q^{76} + 3q^{78} - 156q^{82} - 45q^{84} - 126q^{88} + 24q^{90} - 108q^{91} - 48q^{94} + 138q^{96} - 24q^{97} - 66q^{99} + O(q^{100}) \)

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.bu.a \(12\) \(3.641\) 12.0.\(\cdots\).1 \(\Q(\sqrt{-2}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{11}q^{2}+(-\beta _{1}+\beta _{10})q^{3}-2\beta _{4}q^{4}+\cdots\)
456.2.bu.b \(12\) \(3.641\) 12.0.\(\cdots\).1 \(\Q(\sqrt{-2}) \) \(0\) \(6\) \(0\) \(0\) \(q-\beta _{11}q^{2}+(-\beta _{3}+\beta _{6}+\beta _{9})q^{3}-2\beta _{4}q^{4}+\cdots\)
456.2.bu.c \(432\) \(3.641\) None \(0\) \(-18\) \(0\) \(0\)