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Properties

Label 1911.2.co
Level $1911$
Weight $2$
Character orbit 1911.co
Rep. character $\chi_{1911}(64,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $792$
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.co (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 637 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(522\)

Dimensions

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

Total New Old
Modular forms 1584 792 792
Cusp forms 1536 792 744
Eisenstein series 48 0 48

Trace form

\( 792 q + 4 q^{3} + 136 q^{4} - 132 q^{9} + O(q^{10}) \) \( 792 q + 4 q^{3} + 136 q^{4} - 132 q^{9} - 8 q^{10} - 12 q^{12} + 8 q^{13} - 12 q^{14} - 112 q^{16} + 8 q^{17} + 16 q^{22} + 140 q^{25} - 24 q^{26} + 4 q^{27} - 8 q^{29} + 60 q^{35} + 136 q^{36} - 60 q^{38} + 30 q^{39} - 16 q^{40} + 8 q^{42} - 16 q^{43} - 168 q^{48} - 16 q^{49} - 20 q^{51} + 46 q^{52} - 24 q^{53} + 84 q^{55} + 156 q^{56} - 68 q^{61} + 4 q^{62} + 296 q^{64} - 36 q^{65} + 16 q^{66} + 16 q^{68} - 8 q^{69} + 40 q^{74} + 4 q^{75} - 44 q^{77} - 28 q^{78} + 40 q^{79} - 132 q^{81} - 48 q^{82} - 108 q^{88} - 8 q^{90} - 20 q^{91} - 108 q^{94} - 192 q^{95} + O(q^{100}) \)

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

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