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Properties

Label 1911.4.e
Level $1911$
Weight $4$
Character orbit 1911.e
Rep. character $\chi_{1911}(1028,\cdot)$
Character field $\Q$
Dimension $480$
Sturm bound $1045$

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Defining parameters

Level: \( N \) \(=\) \( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1911.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Sturm bound: \(1045\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1911, [\chi])\).

Total New Old
Modular forms 800 480 320
Cusp forms 768 480 288
Eisenstein series 32 0 32

Trace form

\( 480 q - 1920 q^{4} + 56 q^{9} + O(q^{10}) \) \( 480 q - 1920 q^{4} + 56 q^{9} - 168 q^{15} + 7200 q^{16} + 140 q^{18} + 720 q^{22} + 11352 q^{25} + 432 q^{30} - 932 q^{36} - 96 q^{37} + 1344 q^{43} - 5280 q^{46} - 2028 q^{51} - 2176 q^{57} + 1488 q^{58} + 3168 q^{60} - 23856 q^{64} - 3264 q^{67} + 604 q^{72} - 1820 q^{78} + 2472 q^{79} + 4056 q^{81} + 9312 q^{85} + 1200 q^{88} + 2816 q^{93} + 4072 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1911, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(1911, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1911, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)