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Properties

Label 1911.4.dw
Level $1911$
Weight $4$
Character orbit 1911.dw
Rep. character $\chi_{1911}(4,\cdot)$
Character field $\Q(\zeta_{42})$
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.dw (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 637 \)
Character field: \(\Q(\zeta_{42})\)
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

\( 4704 q + 6 q^{3} + 3136 q^{4} - 36 q^{7} + 3528 q^{9} + O(q^{10}) \) \( 4704 q + 6 q^{3} + 3136 q^{4} - 36 q^{7} + 3528 q^{9} - 80 q^{10} - 84 q^{11} - 48 q^{12} - 62 q^{13} - 240 q^{14} - 12656 q^{16} + 8 q^{17} - 270 q^{19} + 120 q^{20} - 84 q^{21} + 70 q^{22} - 9800 q^{25} + 2202 q^{26} - 108 q^{27} + 36 q^{28} - 140 q^{29} - 150 q^{31} + 1356 q^{35} - 14112 q^{36} - 588 q^{37} - 3444 q^{38} - 2604 q^{39} + 570 q^{40} + 288 q^{41} + 426 q^{42} + 28 q^{43} - 10080 q^{44} + 180 q^{47} - 2304 q^{48} - 942 q^{49} + 15876 q^{50} + 2184 q^{51} - 1484 q^{52} + 588 q^{53} + 3128 q^{55} + 4062 q^{56} + 3190 q^{61} + 1516 q^{62} - 2916 q^{63} + 50456 q^{64} - 1260 q^{65} + 1056 q^{66} - 798 q^{67} - 4136 q^{68} - 1056 q^{69} + 5706 q^{70} + 1260 q^{71} + 7458 q^{73} + 3640 q^{74} + 1476 q^{75} + 3504 q^{76} - 1016 q^{77} + 5250 q^{78} - 490 q^{79} - 960 q^{80} + 31752 q^{81} + 9724 q^{82} + 1344 q^{84} - 504 q^{85} + 3024 q^{86} - 3240 q^{87} - 9744 q^{88} + 1440 q^{90} - 11588 q^{91} - 2268 q^{92} + 19506 q^{94} + 8400 q^{95} + 3870 q^{96} + 16500 q^{97} - 978 q^{98} + O(q^{100}) \)

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

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