Properties

Label 456.2.u
Level $456$
Weight $2$
Character orbit 456.u
Rep. character $\chi_{456}(11,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $152$
Newform subspaces $4$
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.u (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 456 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(160\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\), \(41\)

Dimensions

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

Total New Old
Modular forms 168 168 0
Cusp forms 152 152 0
Eisenstein series 16 16 0

Trace form

\( 152q - 2q^{3} - 4q^{4} - 5q^{6} - 2q^{9} + O(q^{10}) \) \( 152q - 2q^{3} - 4q^{4} - 5q^{6} - 2q^{9} + 8q^{10} + 2q^{12} - 4q^{16} + 6q^{18} - 16q^{19} + 2q^{22} + 3q^{24} - 64q^{25} - 8q^{27} + 6q^{28} + 4q^{30} - 4q^{33} + 8q^{34} + 25q^{36} - 40q^{40} - 18q^{42} - 4q^{43} - 16q^{46} - 19q^{48} - 136q^{49} - 14q^{51} - 26q^{52} - 2q^{54} - 2q^{57} + 64q^{58} - 18q^{60} - 112q^{64} + 9q^{66} - 4q^{67} + 72q^{70} - 29q^{72} + 4q^{73} + 136q^{75} + 32q^{76} - 50q^{78} - 6q^{81} - 54q^{82} + 36q^{84} + 68q^{88} - 22q^{90} + 24q^{91} - 8q^{94} - 98q^{96} + 12q^{97} + 48q^{99} + O(q^{100}) \)

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.u.a \(4\) \(3.641\) \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) \(0\) \(-4\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(-1+\beta _{3})q^{3}+2\beta _{2}q^{4}+\cdots\)
456.2.u.b \(4\) \(3.641\) \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) \(0\) \(2\) \(0\) \(0\) \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{3}+2\beta _{2}q^{4}+\cdots\)
456.2.u.c \(8\) \(3.641\) 8.0.4857532416.1 None \(0\) \(2\) \(0\) \(0\) \(q+(-\beta _{1}-\beta _{7})q^{2}-\beta _{3}q^{3}+(-2+2\beta _{6}+\cdots)q^{4}+\cdots\)
456.2.u.d \(136\) \(3.641\) None \(0\) \(-2\) \(0\) \(0\)