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Properties

Label 1911.4.ct
Level $1911$
Weight $4$
Character orbit 1911.ct
Rep. character $\chi_{1911}(235,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $4032$
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.ct (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(1045\)

Dimensions

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

Total New Old
Modular forms 9456 4032 5424
Cusp forms 9360 4032 5328
Eisenstein series 96 0 96

Trace form

\( 4032 q + 1344 q^{4} - 16 q^{5} - 48 q^{6} + 4 q^{7} + 168 q^{8} + 3024 q^{9} + O(q^{10}) \) \( 4032 q + 1344 q^{4} - 16 q^{5} - 48 q^{6} + 4 q^{7} + 168 q^{8} + 3024 q^{9} + 12 q^{10} + 448 q^{11} - 104 q^{13} - 92 q^{14} + 420 q^{15} + 5376 q^{16} + 636 q^{17} - 1824 q^{19} + 112 q^{20} + 728 q^{22} - 112 q^{23} + 288 q^{24} + 8372 q^{25} - 1100 q^{28} + 168 q^{29} - 336 q^{30} - 4364 q^{31} - 5376 q^{32} + 300 q^{33} - 1328 q^{34} + 1616 q^{35} - 24192 q^{36} - 168 q^{37} - 2580 q^{38} - 3120 q^{40} - 640 q^{41} + 168 q^{42} + 560 q^{43} + 896 q^{44} + 1872 q^{45} + 5680 q^{47} - 1056 q^{48} + 1712 q^{49} - 3304 q^{50} + 2184 q^{51} + 624 q^{52} + 2324 q^{53} + 216 q^{54} - 1132 q^{55} - 3656 q^{56} - 6076 q^{58} - 5632 q^{59} - 13104 q^{60} + 452 q^{61} - 3288 q^{62} - 288 q^{63} - 43848 q^{64} - 1368 q^{66} + 1960 q^{67} - 6028 q^{68} - 1296 q^{69} + 8508 q^{70} - 1568 q^{71} - 6048 q^{72} - 1592 q^{73} - 3276 q^{74} - 12012 q^{76} - 120 q^{77} - 588 q^{79} - 20448 q^{80} + 27216 q^{81} - 3712 q^{82} - 27096 q^{83} + 6384 q^{84} + 1008 q^{85} - 10360 q^{86} + 7584 q^{87} + 12096 q^{88} + 3440 q^{89} - 216 q^{90} + 624 q^{91} - 1512 q^{92} - 3832 q^{94} + 4928 q^{95} + 2688 q^{96} + 21672 q^{97} + 20844 q^{98} - 1008 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1911, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(637, [\chi])\)\(^{\oplus 2}\)