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Properties

Label 1911.2.eo
Level $1911$
Weight $2$
Character orbit 1911.eo
Rep. character $\chi_{1911}(136,\cdot)$
Character field $\Q(\zeta_{84})$
Dimension $3144$
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.eo (of order \(84\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 637 \)
Character field: \(\Q(\zeta_{84})\)
Sturm bound: \(522\)

Dimensions

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

Total New Old
Modular forms 6360 3144 3216
Cusp forms 6168 3144 3024
Eisenstein series 192 0 192

Trace form

\( 3144 q - 4 q^{7} - 262 q^{9} + O(q^{10}) \) \( 3144 q - 4 q^{7} - 262 q^{9} + 16 q^{11} - 8 q^{12} - 24 q^{14} + 536 q^{16} + 32 q^{19} + 12 q^{21} - 8 q^{22} + 132 q^{24} + 60 q^{26} + 136 q^{28} - 8 q^{29} + 2 q^{31} + 40 q^{32} - 112 q^{34} - 48 q^{35} + 86 q^{37} + 12 q^{39} + 60 q^{40} - 36 q^{41} + 12 q^{42} + 36 q^{43} - 112 q^{44} - 16 q^{46} + 168 q^{47} - 44 q^{49} - 432 q^{50} + 96 q^{52} + 24 q^{53} + 72 q^{55} - 432 q^{56} + 38 q^{57} + 208 q^{59} + 20 q^{60} + 72 q^{61} + 72 q^{62} + 12 q^{63} - 672 q^{64} + 72 q^{65} + 8 q^{67} + 168 q^{70} - 244 q^{71} + 130 q^{73} + 40 q^{74} - 28 q^{75} - 76 q^{76} - 8 q^{79} - 204 q^{80} + 262 q^{81} - 48 q^{82} + 48 q^{83} - 20 q^{84} + 92 q^{85} + 312 q^{86} - 72 q^{88} - 48 q^{89} - 276 q^{91} - 72 q^{92} - 34 q^{93} + 148 q^{94} + 96 q^{96} + 406 q^{97} - 356 q^{98} + 8 q^{99} + O(q^{100}) \)

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

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