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Properties

Label 1911.4.l
Level $1911$
Weight $4$
Character orbit 1911.l
Rep. character $\chi_{1911}(802,\cdot)$
Character field $\Q(\zeta_{3})$
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.l (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{3})\)
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

\( 560 q - 6 q^{3} + 2240 q^{4} - 2520 q^{9} + O(q^{10}) \) \( 560 q - 6 q^{3} + 2240 q^{4} - 2520 q^{9} - 80 q^{10} - 28 q^{11} - 48 q^{12} + 62 q^{13} + 9072 q^{16} - 8 q^{17} - 114 q^{19} + 40 q^{20} - 182 q^{22} + 352 q^{23} + 180 q^{24} - 7128 q^{25} - 638 q^{26} + 108 q^{27} - 172 q^{29} + 178 q^{31} - 280 q^{32} + 1864 q^{34} - 10080 q^{36} + 784 q^{37} - 468 q^{38} - 798 q^{39} - 1350 q^{40} + 792 q^{41} + 392 q^{43} + 280 q^{44} + 808 q^{46} - 24 q^{47} - 384 q^{48} - 1986 q^{50} + 288 q^{51} - 4 q^{52} + 244 q^{53} - 1484 q^{55} - 1176 q^{57} + 936 q^{58} - 3008 q^{59} + 804 q^{60} - 2684 q^{61} + 844 q^{62} + 37384 q^{64} - 2932 q^{65} - 1056 q^{66} + 902 q^{67} + 3944 q^{68} - 1152 q^{69} - 1668 q^{71} + 598 q^{73} - 2704 q^{74} + 2724 q^{75} - 1376 q^{76} - 1530 q^{78} - 1198 q^{79} - 1156 q^{80} - 22680 q^{81} - 1766 q^{82} + 2896 q^{83} - 1928 q^{85} - 1960 q^{86} + 5112 q^{87} - 2472 q^{88} + 6544 q^{89} + 1440 q^{90} + 14452 q^{92} + 4116 q^{93} - 4552 q^{94} + 6816 q^{95} + 2730 q^{96} + 400 q^{97} + 504 q^{99} + O(q^{100}) \)

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

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