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Properties

Label 1911.2.ch
Level $1911$
Weight $2$
Character orbit 1911.ch
Rep. character $\chi_{1911}(19,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $372$
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.ch (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
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 372 736
Cusp forms 980 372 608
Eisenstein series 128 0 128

Trace form

\( 372 q - 372 q^{9} + O(q^{10}) \) \( 372 q - 372 q^{9} - 8 q^{11} + 8 q^{12} + 180 q^{16} + 10 q^{19} - 8 q^{22} + 60 q^{26} - 24 q^{29} - 8 q^{31} - 20 q^{32} + 12 q^{37} + 12 q^{39} + 60 q^{40} + 36 q^{41} - 48 q^{43} + 64 q^{44} + 36 q^{46} + 120 q^{50} - 48 q^{51} - 100 q^{52} + 8 q^{53} + 12 q^{55} + 10 q^{57} + 32 q^{58} + 68 q^{60} - 72 q^{62} - 40 q^{65} - 82 q^{67} + 72 q^{68} - 52 q^{71} + 38 q^{73} - 40 q^{74} - 14 q^{75} + 76 q^{76} + 16 q^{78} + 8 q^{79} - 96 q^{80} + 372 q^{81} - 96 q^{82} - 48 q^{83} - 100 q^{85} + 48 q^{86} - 36 q^{87} - 48 q^{89} - 200 q^{92} - 14 q^{93} - 48 q^{95} - 12 q^{96} + 98 q^{97} + 8 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1911, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(637, [\chi])\)\(^{\oplus 2}\)