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Properties

Label 1911.4.bf
Level $1911$
Weight $4$
Character orbit 1911.bf
Rep. character $\chi_{1911}(1244,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $1104$
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.bf (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 273 \)
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 1136 464
Cusp forms 1536 1104 432
Eisenstein series 64 32 32

Trace form

\( 1104 q + 2174 q^{4} + 48 q^{6} + 66 q^{9} + O(q^{10}) \) \( 1104 q + 2174 q^{4} + 48 q^{6} + 66 q^{9} - 18 q^{12} - 90 q^{13} - 167 q^{15} - 8434 q^{16} + 74 q^{18} + 86 q^{22} - 12996 q^{25} + 1092 q^{30} - 498 q^{31} + 994 q^{36} - 562 q^{37} - 86 q^{39} - 366 q^{40} - 376 q^{43} + 3 q^{45} + 320 q^{46} - 306 q^{48} + 924 q^{51} - 2580 q^{52} + 207 q^{54} - 1110 q^{55} - 2614 q^{57} - 2476 q^{58} + 2631 q^{60} - 62648 q^{64} - 1173 q^{66} - 4752 q^{67} - 1254 q^{69} - 7470 q^{72} + 1722 q^{73} - 4968 q^{75} + 864 q^{76} - 9131 q^{78} + 3486 q^{79} - 966 q^{81} + 6 q^{85} - 147 q^{87} - 2252 q^{88} + 879 q^{93} - 2442 q^{96} + 24 q^{97} - 4402 q^{99} + O(q^{100}) \)

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

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