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Properties

Label 1911.4.bu
Level $1911$
Weight $4$
Character orbit 1911.bu
Rep. character $\chi_{1911}(1060,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1120$
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.bu (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
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 1120 2080
Cusp forms 3072 1120 1952
Eisenstein series 128 0 128

Trace form

\( 1120 q + 5040 q^{9} + O(q^{10}) \) \( 1120 q + 5040 q^{9} - 112 q^{11} - 192 q^{12} - 17920 q^{16} + 768 q^{19} - 112 q^{22} + 540 q^{24} - 1500 q^{26} - 216 q^{29} + 180 q^{31} - 280 q^{32} - 2128 q^{37} + 1596 q^{39} - 2340 q^{40} + 2088 q^{41} + 1176 q^{43} - 1792 q^{44} - 3168 q^{46} - 5736 q^{50} - 720 q^{51} + 1584 q^{52} - 2264 q^{53} - 1656 q^{55} - 1176 q^{57} + 6432 q^{58} - 4128 q^{59} + 5316 q^{60} - 1800 q^{61} - 4176 q^{62} - 3560 q^{65} + 2944 q^{67} + 856 q^{71} - 3168 q^{73} - 416 q^{74} - 4200 q^{75} + 432 q^{76} - 1968 q^{78} + 2000 q^{79} - 6348 q^{80} - 45360 q^{81} + 864 q^{82} - 3792 q^{83} - 3040 q^{85} + 4032 q^{86} + 10800 q^{88} + 4224 q^{89} + 17816 q^{92} + 4116 q^{93} + 14412 q^{94} + 4320 q^{96} - 1512 q^{97} - 504 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1911, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(637, [\chi])\)\(^{\oplus 2}\)