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Properties

Label 1911.4.bx
Level $1911$
Weight $4$
Character orbit 1911.bx
Rep. character $\chi_{1911}(422,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $2208$
Sturm bound $1045$

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Defining parameters

Level: \( N \) \(=\) \( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1911.bx (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 273 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1045\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1911, [\chi])\).

Total New Old
Modular forms 3200 2272 928
Cusp forms 3072 2208 864
Eisenstein series 128 64 64

Trace form

\( 2208 q + 4 q^{3} + 12 q^{4} - 8 q^{6} + 4 q^{9} + O(q^{10}) \) \( 2208 q + 4 q^{3} + 12 q^{4} - 8 q^{6} + 4 q^{9} + 324 q^{12} + 16 q^{13} - 326 q^{15} + 16892 q^{16} + 322 q^{18} + 608 q^{19} - 16 q^{22} + 172 q^{24} - 536 q^{27} - 564 q^{31} + 178 q^{33} + 408 q^{34} - 3096 q^{36} - 1032 q^{37} + 2504 q^{39} + 276 q^{40} + 2136 q^{43} - 1078 q^{45} + 1512 q^{46} + 280 q^{48} + 648 q^{51} + 1700 q^{52} + 226 q^{54} - 232 q^{55} + 2582 q^{57} - 2860 q^{58} - 2748 q^{60} - 376 q^{61} + 3130 q^{66} + 3704 q^{67} - 1836 q^{69} - 11246 q^{72} + 152 q^{73} + 330 q^{75} - 9120 q^{76} + 2934 q^{78} - 4072 q^{79} + 5700 q^{81} + 7908 q^{85} - 1534 q^{87} + 1650 q^{93} + 9680 q^{94} - 3198 q^{96} - 3672 q^{97} + 5646 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1911, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1911, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1911, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)