↑

Properties

Label 1155.2.da
Level $1155$
Weight $2$
Character orbit 1155.da
Rep. character $\chi_{1155}(4,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $768$
Sturm bound $384$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1155.da (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 385 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1155, [\chi])\).

Total New Old
Modular forms 1600 768 832
Cusp forms 1472 768 704
Eisenstein series 128 0 128

Trace form

\( 768 q - 96 q^{4} - 4 q^{5} + 16 q^{6} - 96 q^{9} + O(q^{10}) \) \( 768 q - 96 q^{4} - 4 q^{5} + 16 q^{6} - 96 q^{9} - 4 q^{10} + 28 q^{14} - 12 q^{15} + 88 q^{16} + 40 q^{19} - 32 q^{20} + 24 q^{24} - 4 q^{25} + 8 q^{26} + 8 q^{30} - 12 q^{31} + 64 q^{34} - 68 q^{35} - 192 q^{36} - 18 q^{40} - 120 q^{41} + 172 q^{44} + 4 q^{45} - 96 q^{46} - 44 q^{49} + 12 q^{51} - 32 q^{54} + 72 q^{55} - 48 q^{56} - 84 q^{61} + 280 q^{64} + 40 q^{65} - 12 q^{66} - 16 q^{69} + 38 q^{70} - 64 q^{71} - 128 q^{74} - 8 q^{75} - 688 q^{76} + 192 q^{80} + 96 q^{81} - 24 q^{84} + 52 q^{85} - 32 q^{86} - 48 q^{89} - 8 q^{90} - 92 q^{91} + 76 q^{94} + 54 q^{95} - 56 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1155, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1155, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1155, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 2}\)