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Properties

Label 1911.4.cq
Level $1911$
Weight $4$
Character orbit 1911.cq
Rep. character $\chi_{1911}(16,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $4704$
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.cq (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 637 \)
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 4704 4752
Cusp forms 9360 4704 4656
Eisenstein series 96 0 96

Trace form

\( 4704 q - 6 q^{3} - 3136 q^{4} - 4 q^{7} + 3528 q^{9} + O(q^{10}) \) \( 4704 q - 6 q^{3} - 3136 q^{4} - 4 q^{7} + 3528 q^{9} - 80 q^{10} - 28 q^{11} - 48 q^{12} + 62 q^{13} - 256 q^{14} - 12432 q^{16} - 8 q^{17} - 114 q^{19} + 40 q^{20} + 168 q^{21} - 182 q^{22} - 2340 q^{24} + 9800 q^{25} - 1702 q^{26} + 108 q^{27} - 480 q^{28} - 140 q^{29} + 178 q^{31} - 280 q^{32} - 3400 q^{34} + 1764 q^{35} + 14112 q^{36} - 1792 q^{37} + 3004 q^{38} - 2604 q^{39} - 1350 q^{40} + 792 q^{41} - 894 q^{42} + 28 q^{43} + 9296 q^{44} + 1288 q^{46} + 60 q^{47} + 2304 q^{48} + 2434 q^{49} + 5292 q^{50} - 2184 q^{51} + 52 q^{52} + 588 q^{53} - 392 q^{55} - 1526 q^{56} - 504 q^{57} + 12336 q^{59} - 420 q^{60} - 2782 q^{61} - 2908 q^{62} + 540 q^{63} - 49896 q^{64} - 1932 q^{65} - 1056 q^{66} + 1750 q^{67} + 3944 q^{68} - 1152 q^{69} + 7934 q^{70} + 1372 q^{71} - 2090 q^{73} + 3640 q^{74} + 2724 q^{75} - 1376 q^{76} - 3400 q^{77} - 5250 q^{78} + 154 q^{79} - 1156 q^{80} + 31752 q^{81} + 32604 q^{82} + 2896 q^{83} + 1968 q^{84} + 3192 q^{85} - 784 q^{86} + 5112 q^{87} + 7728 q^{88} + 6544 q^{89} + 1440 q^{90} - 10772 q^{91} + 8820 q^{92} - 3276 q^{93} - 10894 q^{94} - 6160 q^{95} + 12810 q^{96} - 3548 q^{97} + 29638 q^{98} + 504 q^{99} + O(q^{100}) \)

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

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