Properties

Label 456.3.s
Level $456$
Weight $3$
Character orbit 456.s
Rep. character $\chi_{456}(107,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $312$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 456.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 456 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(456, [\chi])\).

Total New Old
Modular forms 328 328 0
Cusp forms 312 312 0
Eisenstein series 16 16 0

Trace form

\( 312q - 6q^{3} - 4q^{4} + 7q^{6} - 2q^{9} + O(q^{10}) \) \( 312q - 6q^{3} - 4q^{4} + 7q^{6} - 2q^{9} + 24q^{10} + 12q^{16} - 40q^{19} + 18q^{22} - 53q^{24} - 704q^{25} + 30q^{28} + 136q^{30} + 48q^{33} + 36q^{34} - 35q^{36} + 144q^{40} - 16q^{42} - 4q^{43} + 63q^{48} - 1896q^{49} - 6q^{51} + 114q^{52} - 16q^{54} + 18q^{57} + 40q^{58} - 174q^{60} + 704q^{64} + 31q^{66} - 12q^{67} + 720q^{70} - 237q^{72} - 84q^{73} + 620q^{76} + 402q^{78} + 54q^{81} - 54q^{82} + 330q^{90} + 576q^{91} - 442q^{96} - 12q^{97} + 32q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(456, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.