Properties

Label 1911.4.ei
Level $1911$
Weight $4$
Character orbit 1911.ei
Rep. character $\chi_{1911}(73,\cdot)$
Character field $\Q(\zeta_{84})$
Dimension $9408$
Sturm bound $1045$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1911.ei (of order \(84\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 637 \)
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 9408 9504
Cusp forms 18720 9408 9312
Eisenstein series 192 0 192

Trace form

\( 9408 q + 44 q^{7} - 7056 q^{9} + O(q^{10}) \) \( 9408 q + 44 q^{7} - 7056 q^{9} + 56 q^{11} - 912 q^{14} - 12544 q^{16} - 204 q^{19} - 216 q^{21} + 224 q^{22} + 720 q^{24} - 1500 q^{26} + 244 q^{28} + 560 q^{29} - 300 q^{31} + 140 q^{32} - 5264 q^{34} + 6240 q^{35} + 2128 q^{37} - 1008 q^{39} + 4680 q^{40} - 936 q^{42} + 1120 q^{44} - 336 q^{46} - 168 q^{47} + 21168 q^{50} + 4364 q^{52} - 1176 q^{53} - 4368 q^{55} - 840 q^{57} - 3544 q^{59} + 420 q^{60} + 1800 q^{61} - 216 q^{63} + 2016 q^{65} - 1036 q^{67} + 288 q^{68} - 476 q^{70} + 2800 q^{71} - 5052 q^{73} - 23296 q^{74} - 336 q^{79} + 2508 q^{80} + 63504 q^{81} + 3312 q^{84} + 336 q^{85} + 1680 q^{86} + 5616 q^{87} + 4224 q^{89} - 4844 q^{91} - 13104 q^{92} + 420 q^{93} + 3528 q^{94} - 13500 q^{96} - 73168 q^{98} + 1008 q^{99} + O(q^{100}) \)

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

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