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Properties

Label 1911.2.bx
Level $1911$
Weight $2$
Character orbit 1911.bx
Rep. character $\chi_{1911}(422,\cdot)$
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.bx (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

\( 716 q + 4 q^{3} + 12 q^{4} + 4 q^{6} + 4 q^{9} + O(q^{10}) \) \( 716 q + 4 q^{3} + 12 q^{4} + 4 q^{6} + 4 q^{9} + 36 q^{12} + 16 q^{13} - 14 q^{15} + 312 q^{16} + 34 q^{18} + 14 q^{19} - 16 q^{22} + 4 q^{24} + 40 q^{27} + 12 q^{31} - 50 q^{33} + 48 q^{34} + 72 q^{36} + 20 q^{37} - 40 q^{39} - 44 q^{40} - 48 q^{43} - 58 q^{45} - 16 q^{46} + 64 q^{48} + 72 q^{51} + 20 q^{52} + 22 q^{54} + 16 q^{55} - 58 q^{57} + 36 q^{58} + 24 q^{60} + 40 q^{61} + 34 q^{66} - 26 q^{67} + 54 q^{69} + 130 q^{72} - 62 q^{73} + 42 q^{75} - 116 q^{76} - 114 q^{78} + 48 q^{79} - 12 q^{81} - 152 q^{85} + 2 q^{87} - 120 q^{93} - 32 q^{94} + 54 q^{96} - 62 q^{97} + 6 q^{99} + O(q^{100}) \)

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

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