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Properties

Label 1911.4.n
Level $1911$
Weight $4$
Character orbit 1911.n
Rep. character $\chi_{1911}(785,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $1128$
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.n (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
Character field: \(\Q(i)\)
Sturm bound: \(1045\)

Dimensions

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

Total New Old
Modular forms 1600 1168 432
Cusp forms 1536 1128 408
Eisenstein series 64 40 24

Trace form

\( 1128 q + 4 q^{3} + 16 q^{6} + 4 q^{9} + O(q^{10}) \) \( 1128 q + 4 q^{3} + 16 q^{6} + 4 q^{9} - 68 q^{13} + 64 q^{15} - 17152 q^{16} + 172 q^{18} - 196 q^{19} - 256 q^{22} - 292 q^{24} - 32 q^{27} - 348 q^{31} - 368 q^{33} + 528 q^{34} + 864 q^{37} + 240 q^{39} - 840 q^{40} - 156 q^{45} - 360 q^{46} - 1412 q^{48} - 1336 q^{52} - 500 q^{54} - 1336 q^{55} - 1416 q^{57} + 1232 q^{58} + 40 q^{60} + 1784 q^{61} - 1080 q^{66} + 764 q^{67} - 796 q^{72} - 2512 q^{73} - 1920 q^{76} - 2392 q^{78} - 1600 q^{79} - 2572 q^{81} - 3096 q^{85} + 4976 q^{87} - 2992 q^{93} + 13304 q^{94} - 52 q^{96} + 48 q^{97} - 8344 q^{99} + O(q^{100}) \)

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

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