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Properties

Label 1911.4.bw
Level $1911$
Weight $4$
Character orbit 1911.bw
Rep. character $\chi_{1911}(128,\cdot)$
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.bw (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

\( 2208 q - 2 q^{3} - 8 q^{6} - 2 q^{9} + O(q^{10}) \) \( 2208 q - 2 q^{3} - 8 q^{6} - 2 q^{9} + 12 q^{10} - 324 q^{12} + 16 q^{13} - 326 q^{15} - 33784 q^{16} - 110 q^{18} - 4 q^{19} - 16 q^{22} - 50 q^{24} - 536 q^{27} - 1626 q^{30} + 456 q^{31} - 458 q^{33} + 408 q^{34} - 3096 q^{36} - 1116 q^{37} - 2794 q^{39} + 276 q^{40} + 2136 q^{43} + 422 q^{45} - 312 q^{46} + 280 q^{48} - 648 q^{51} - 3340 q^{52} - 134 q^{54} - 232 q^{55} + 2582 q^{57} + 5540 q^{58} + 2358 q^{60} + 188 q^{61} + 3130 q^{66} - 4444 q^{67} - 1836 q^{69} + 9370 q^{72} - 1060 q^{73} - 9120 q^{76} + 2934 q^{78} - 4072 q^{79} - 2850 q^{81} + 876 q^{82} + 7908 q^{85} + 3068 q^{87} + 1308 q^{88} - 1662 q^{93} - 4840 q^{94} - 2298 q^{96} - 3672 q^{97} + 5646 q^{99} + O(q^{100}) \)

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

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