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Properties

Label 1911.4.cd
Level $1911$
Weight $4$
Character orbit 1911.cd
Rep. character $\chi_{1911}(50,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $2256$
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.cd (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 39 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1045\)

Dimensions

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

Total New Old
Modular forms 3200 2336 864
Cusp forms 3072 2256 816
Eisenstein series 128 80 48

Trace form

\( 2256 q + 2 q^{3} + 12 q^{4} - 10 q^{6} + 2 q^{9} + O(q^{10}) \) \( 2256 q + 2 q^{3} + 12 q^{4} - 10 q^{6} + 2 q^{9} - 132 q^{10} - 64 q^{13} - 94 q^{15} + 17164 q^{16} + 392 q^{18} - 212 q^{19} + 196 q^{22} - 758 q^{24} + 872 q^{27} + 582 q^{30} + 612 q^{31} - 226 q^{33} - 84 q^{34} - 36 q^{36} + 1668 q^{37} + 678 q^{39} + 4536 q^{40} + 24 q^{43} + 282 q^{45} + 1200 q^{46} - 838 q^{48} - 3008 q^{52} + 2114 q^{54} - 524 q^{55} + 1146 q^{57} - 1652 q^{58} - 616 q^{60} + 1036 q^{61} + 1416 q^{66} - 1472 q^{67} + 2034 q^{69} + 5044 q^{72} - 644 q^{73} + 5484 q^{75} - 192 q^{76} - 2168 q^{78} + 2416 q^{79} - 3038 q^{81} + 4296 q^{82} + 6348 q^{85} + 1738 q^{87} + 8436 q^{88} - 3374 q^{93} + 1216 q^{94} + 3436 q^{96} + 5388 q^{97} - 3074 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1911, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(273, [\chi])\)\(^{\oplus 2}\)