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Properties

Label 1911.2.bw
Level $1911$
Weight $2$
Character orbit 1911.bw
Rep. character $\chi_{1911}(128,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $716$
Sturm bound $522$

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Defining parameters

Level: \( N \) \(=\) \( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1911.bw (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 273 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(522\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1911, [\chi])\).

Total New Old
Modular forms 1108 780 328
Cusp forms 980 716 264
Eisenstein series 128 64 64

Trace form

\( 716 q - 2 q^{3} + 4 q^{6} - 2 q^{9} + O(q^{10}) \) \( 716 q - 2 q^{3} + 4 q^{6} - 2 q^{9} + 12 q^{10} - 36 q^{12} + 16 q^{13} - 14 q^{15} - 624 q^{16} - 38 q^{18} + 20 q^{19} - 16 q^{22} - 2 q^{24} + 40 q^{27} - 42 q^{30} - 42 q^{31} + 16 q^{33} + 48 q^{34} + 72 q^{36} + 14 q^{37} - 10 q^{39} - 44 q^{40} - 48 q^{43} + 2 q^{45} - 64 q^{46} + 64 q^{48} - 72 q^{51} - 40 q^{52} - 14 q^{54} + 16 q^{55} - 58 q^{57} - 84 q^{58} + 198 q^{60} - 20 q^{61} + 34 q^{66} + 16 q^{67} + 54 q^{69} + 46 q^{72} + 82 q^{73} - 116 q^{76} - 114 q^{78} + 48 q^{79} + 6 q^{81} - 36 q^{82} - 152 q^{85} - 4 q^{87} - 204 q^{88} + 6 q^{93} + 16 q^{94} + 90 q^{96} - 62 q^{97} + 6 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1911, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1911, [\chi])\) into lower level spaces

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