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Properties

Label 1911.4.el
Level $1911$
Weight $4$
Character orbit 1911.el
Rep. character $\chi_{1911}(11,\cdot)$
Character field $\Q(\zeta_{84})$
Dimension $18720$
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.el (of order \(84\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1911 \)
Character field: \(\Q(\zeta_{84})\)
Sturm bound: \(1045\)

Dimensions

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

Total New Old
Modular forms 18912 18912 0
Cusp forms 18720 18720 0
Eisenstein series 192 192 0

Trace form

\( 18720 q - 10 q^{3} - 72 q^{4} - 36 q^{6} - 40 q^{7} - 10 q^{9} + O(q^{10}) \) \( 18720 q - 10 q^{3} - 72 q^{4} - 36 q^{6} - 40 q^{7} - 10 q^{9} - 84 q^{10} + 324 q^{12} - 40 q^{13} - 74 q^{15} - 24608 q^{16} + 148 q^{18} + 580 q^{19} + 44 q^{21} - 20 q^{22} + 144 q^{24} - 592 q^{27} - 872 q^{28} - 592 q^{31} + 150 q^{33} + 352 q^{34} - 30 q^{36} - 4392 q^{37} + 28 q^{39} + 164 q^{40} + 2222 q^{42} + 612 q^{43} - 826 q^{45} + 304 q^{46} + 252 q^{48} - 1080 q^{49} - 324 q^{51} - 11908 q^{52} + 198 q^{54} - 260 q^{55} + 412 q^{57} + 12 q^{58} - 916 q^{60} - 404 q^{61} + 3312 q^{63} + 10774 q^{66} + 1180 q^{67} - 1878 q^{69} + 4148 q^{70} - 3066 q^{72} + 96 q^{73} + 288 q^{75} - 5592 q^{76} + 5778 q^{78} - 384 q^{79} - 1802 q^{81} - 84 q^{82} + 1276 q^{84} - 212 q^{85} - 3004 q^{87} - 84 q^{88} - 4996 q^{91} - 5830 q^{93} - 7820 q^{94} + 8506 q^{96} - 3784 q^{97} - 1506 q^{99} + O(q^{100}) \)

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.