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Properties

Label 1911.2.cm
Level $1911$
Weight $2$
Character orbit 1911.cm
Rep. character $\chi_{1911}(209,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $1344$
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.cm (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 147 \)
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 1344 240
Cusp forms 1536 1344 192
Eisenstein series 48 0 48

Trace form

\( 1344 q + 224 q^{4} - 28 q^{6} - 4 q^{7} - 20 q^{9} + O(q^{10}) \) \( 1344 q + 224 q^{4} - 28 q^{6} - 4 q^{7} - 20 q^{9} + 70 q^{12} + 12 q^{15} - 224 q^{16} + 20 q^{18} + 4 q^{21} - 20 q^{22} - 200 q^{25} + 42 q^{27} + 28 q^{28} + 4 q^{30} + 112 q^{34} + 80 q^{36} - 16 q^{37} + 28 q^{40} - 112 q^{42} - 32 q^{43} - 112 q^{45} - 120 q^{46} - 4 q^{49} + 16 q^{51} + 84 q^{55} + 18 q^{57} + 132 q^{58} - 188 q^{60} - 8 q^{63} + 176 q^{64} - 126 q^{66} - 20 q^{70} - 84 q^{72} - 210 q^{75} - 336 q^{76} + 50 q^{78} + 64 q^{79} + 156 q^{81} - 274 q^{84} + 32 q^{85} - 72 q^{88} - 42 q^{90} - 4 q^{91} - 108 q^{93} - 168 q^{94} - 238 q^{96} - 260 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1911, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)