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Properties

Label 1911.4.t
Level $1911$
Weight $4$
Character orbit 1911.t
Rep. character $\chi_{1911}(1096,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $560$
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.t (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1045\)

Dimensions

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

Total New Old
Modular forms 1600 560 1040
Cusp forms 1536 560 976
Eisenstein series 64 0 64

Trace form

\( 560 q + 6 q^{3} - 2240 q^{4} - 2520 q^{9} + O(q^{10}) \) \( 560 q + 6 q^{3} - 2240 q^{4} - 2520 q^{9} - 80 q^{10} - 84 q^{11} - 48 q^{12} - 62 q^{13} + 8848 q^{16} + 8 q^{17} - 270 q^{19} + 120 q^{20} + 70 q^{22} - 352 q^{23} + 7128 q^{25} + 1138 q^{26} - 108 q^{27} - 172 q^{29} - 150 q^{31} + 10080 q^{36} + 28 q^{38} - 798 q^{39} + 570 q^{40} + 288 q^{41} - 840 q^{43} + 2856 q^{44} - 72 q^{47} + 384 q^{48} + 666 q^{50} - 48 q^{51} - 1540 q^{52} + 2020 q^{53} + 2036 q^{55} + 5688 q^{58} + 3672 q^{60} + 3092 q^{61} - 2236 q^{62} - 30552 q^{64} - 2308 q^{65} + 1056 q^{66} - 2790 q^{67} - 4136 q^{68} - 1056 q^{69} + 1260 q^{71} - 606 q^{73} - 2704 q^{74} + 1476 q^{75} + 3504 q^{76} - 438 q^{78} + 3198 q^{79} - 960 q^{80} - 22680 q^{81} - 4626 q^{82} - 696 q^{85} - 504 q^{86} - 3240 q^{87} - 1128 q^{88} + 1440 q^{90} + 3364 q^{92} + 4428 q^{94} - 4576 q^{95} + 3870 q^{96} + 4656 q^{97} + O(q^{100}) \)

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

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