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Properties

Label 456.3.bn
Level $456$
Weight $3$
Character orbit 456.bn
Rep. character $\chi_{456}(13,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $480$
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.bn (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 152 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(240\)

Dimensions

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

Total New Old
Modular forms 984 480 504
Cusp forms 936 480 456
Eisenstein series 48 0 48

Trace form

\( 480 q + 6 q^{4} - 18 q^{6} + O(q^{10}) \) \( 480 q + 6 q^{4} - 18 q^{6} - 84 q^{10} - 90 q^{14} + 42 q^{16} - 60 q^{20} + 324 q^{28} + 90 q^{32} - 174 q^{34} + 18 q^{36} + 72 q^{38} + 18 q^{40} - 420 q^{44} + 810 q^{46} - 576 q^{47} + 72 q^{48} - 1680 q^{49} + 702 q^{50} + 390 q^{52} - 54 q^{54} - 72 q^{58} + 180 q^{60} + 660 q^{62} + 174 q^{64} + 432 q^{66} + 474 q^{68} + 108 q^{70} + 108 q^{72} + 240 q^{73} + 96 q^{74} - 72 q^{76} + 144 q^{78} + 6 q^{80} + 378 q^{82} - 972 q^{84} - 624 q^{86} - 936 q^{88} - 18 q^{90} - 1440 q^{92} - 960 q^{95} - 1056 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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

Decomposition of \(S_{3}^{\mathrm{old}}(456, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(456, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 2}\)