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Properties

Label 1911.2.dm
Level $1911$
Weight $2$
Character orbit 1911.dm
Rep. character $\chi_{1911}(43,\cdot)$
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.dm (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

\( 1560 q - 2 q^{3} - 128 q^{4} + 3 q^{7} + 130 q^{9} + O(q^{10}) \) \( 1560 q - 2 q^{3} - 128 q^{4} + 3 q^{7} + 130 q^{9} + 8 q^{10} + 24 q^{11} - 8 q^{12} - 6 q^{13} + 140 q^{16} - 8 q^{17} - 12 q^{19} - 48 q^{20} + 20 q^{22} + 252 q^{25} - 96 q^{26} + 4 q^{27} - 132 q^{28} + 8 q^{29} + 30 q^{35} - 128 q^{36} + 30 q^{37} - 10 q^{39} + 88 q^{40} + 36 q^{41} + 4 q^{42} - 6 q^{43} + 48 q^{48} + 23 q^{49} + 648 q^{50} - 40 q^{51} - 26 q^{52} - 48 q^{53} + 6 q^{55} + 84 q^{56} + 96 q^{59} + 13 q^{61} + 32 q^{62} + 18 q^{63} + 24 q^{64} + 36 q^{65} + 32 q^{66} - 6 q^{67} - 16 q^{68} + 8 q^{69} + 36 q^{71} + 20 q^{74} + 30 q^{75} - 24 q^{76} + 56 q^{77} + 28 q^{78} - 36 q^{79} - 96 q^{80} + 130 q^{81} - 150 q^{82} - 6 q^{84} + 120 q^{85} - 36 q^{87} + 36 q^{88} - 120 q^{89} - 16 q^{90} + 17 q^{91} + 216 q^{92} - 6 q^{93} - 90 q^{94} - 96 q^{95} - 426 q^{97} + O(q^{100}) \)

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

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