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Properties

Label 1911.2.dg
Level $1911$
Weight $2$
Character orbit 1911.dg
Rep. character $\chi_{1911}(25,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $1560$
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.dg (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 637 \)
Character field: \(\Q(\zeta_{42})\)
Sturm bound: \(522\)

Dimensions

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

Total New Old
Modular forms 3192 1560 1632
Cusp forms 3096 1560 1536
Eisenstein series 96 0 96

Trace form

\( 1560 q - 2 q^{3} - 128 q^{4} + 130 q^{9} + O(q^{10}) \) \( 1560 q - 2 q^{3} - 128 q^{4} + 130 q^{9} + 8 q^{10} + 4 q^{12} - 6 q^{13} - 36 q^{14} + 140 q^{16} + 4 q^{17} - 16 q^{22} - 126 q^{25} + 6 q^{26} + 4 q^{27} + 8 q^{29} - 24 q^{35} + 256 q^{36} - 12 q^{38} + 8 q^{39} - 44 q^{40} - 8 q^{42} - 12 q^{43} - 96 q^{48} + 14 q^{49} - 52 q^{51} + 46 q^{52} - 12 q^{53} + 12 q^{55} + 228 q^{56} - 50 q^{61} + 152 q^{62} + 96 q^{64} - 18 q^{65} - 16 q^{66} + 8 q^{68} - 40 q^{69} - 64 q^{74} + 30 q^{75} + 80 q^{77} + 28 q^{78} + 6 q^{79} + 130 q^{81} - 420 q^{82} - 36 q^{87} + 72 q^{88} - 16 q^{90} - 91 q^{91} - 564 q^{94} - 432 q^{95} + O(q^{100}) \)

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

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