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Properties

Label 1155.2.dh
Level $1155$
Weight $2$
Character orbit 1155.dh
Rep. character $\chi_{1155}(19,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $768$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1155.dh (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

\( 768 q + 96 q^{4} + 12 q^{5} + 96 q^{9} + O(q^{10}) \) \( 768 q + 96 q^{4} + 12 q^{5} + 96 q^{9} - 4 q^{14} + 12 q^{15} + 104 q^{16} - 28 q^{25} + 24 q^{26} + 36 q^{31} + 80 q^{35} - 192 q^{36} + 90 q^{40} + 20 q^{44} - 12 q^{45} + 120 q^{46} + 100 q^{49} - 20 q^{51} - 80 q^{56} - 48 q^{59} - 60 q^{61} - 104 q^{64} + 36 q^{66} + 22 q^{70} - 128 q^{71} - 24 q^{75} + 180 q^{80} + 96 q^{81} + 180 q^{85} - 32 q^{86} - 4 q^{91} + 60 q^{94} + 10 q^{95} + O(q^{100}) \)

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

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