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Properties

Label 1911.4.p
Level $1911$
Weight $4$
Character orbit 1911.p
Rep. character $\chi_{1911}(538,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $560$
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.p (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(i)\)
Sturm bound: \(1045\)

Dimensions

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

Total New Old
Modular forms 1600 560 1040
Cusp forms 1536 560 976
Eisenstein series 64 0 64

Trace form

\( 560 q - 5040 q^{9} + O(q^{10}) \) \( 560 q - 5040 q^{9} + 112 q^{11} - 8960 q^{16} - 224 q^{22} - 624 q^{29} + 280 q^{32} + 2296 q^{37} + 1512 q^{39} + 3808 q^{44} - 192 q^{46} + 5736 q^{50} - 1264 q^{53} + 840 q^{57} + 1776 q^{58} + 3288 q^{60} + 6080 q^{65} - 4456 q^{67} - 2704 q^{71} - 8320 q^{74} - 1200 q^{78} - 3008 q^{79} + 45360 q^{81} + 16 q^{85} + 8064 q^{86} + 18736 q^{92} + 840 q^{93} - 1008 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1911, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(637, [\chi])\)\(^{\oplus 2}\)