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Properties

Label 1911.4.ej
Level $1911$
Weight $4$
Character orbit 1911.ej
Rep. character $\chi_{1911}(76,\cdot)$
Character field $\Q(\zeta_{84})$
Dimension $9408$
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.ej (of order \(84\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 637 \)
Character field: \(\Q(\zeta_{84})\)
Sturm bound: \(1045\)

Dimensions

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

Total New Old
Modular forms 18912 9408 9504
Cusp forms 18720 9408 9312
Eisenstein series 192 0 192

Trace form

\( 9408 q - 4 q^{7} - 7056 q^{9} + O(q^{10}) \) \( 9408 q - 4 q^{7} - 7056 q^{9} - 112 q^{11} + 576 q^{14} - 12544 q^{16} - 36 q^{21} + 224 q^{22} + 1260 q^{24} - 752 q^{28} + 560 q^{29} - 280 q^{32} + 10528 q^{34} - 3120 q^{35} + 3388 q^{37} - 2520 q^{39} + 468 q^{42} - 840 q^{43} + 9520 q^{44} - 1848 q^{46} - 168 q^{47} - 2988 q^{49} - 42336 q^{50} - 8176 q^{52} - 4704 q^{53} + 2184 q^{55} - 6804 q^{56} + 1680 q^{57} - 7672 q^{59} + 1680 q^{60} - 2160 q^{63} - 4032 q^{65} + 3584 q^{67} - 7916 q^{70} + 2800 q^{71} - 5376 q^{73} + 7280 q^{74} - 1344 q^{79} + 63504 q^{81} + 3312 q^{84} + 5376 q^{85} + 15792 q^{86} + 12096 q^{88} - 9932 q^{91} - 13104 q^{92} + 7224 q^{93} + 4368 q^{94} + 6720 q^{95} + 20160 q^{96} + 32492 q^{98} + 1008 q^{99} + O(q^{100}) \)

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

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