Properties

Label 1170.2.bo
Level $1170$
Weight $2$
Character orbit 1170.bo
Rep. character $\chi_{1170}(79,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $144$
Sturm bound $504$

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Defining parameters

Level: \( N \) \(=\) \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1170.bo (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(504\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1170, [\chi])\).

Total New Old
Modular forms 520 144 376
Cusp forms 488 144 344
Eisenstein series 32 0 32

Trace form

\( 144 q + 72 q^{4} + 4 q^{5} - 8 q^{6} + 4 q^{9} + O(q^{10}) \) \( 144 q + 72 q^{4} + 4 q^{5} - 8 q^{6} + 4 q^{9} - 8 q^{11} + 4 q^{14} + 24 q^{15} - 72 q^{16} - 4 q^{20} + 56 q^{21} - 4 q^{24} - 12 q^{25} + 24 q^{26} + 4 q^{29} - 12 q^{30} + 24 q^{31} - 36 q^{35} + 8 q^{36} - 36 q^{41} - 16 q^{44} + 20 q^{45} + 24 q^{46} + 84 q^{49} - 16 q^{50} - 60 q^{51} - 28 q^{54} + 48 q^{55} - 4 q^{56} + 40 q^{59} + 24 q^{60} - 12 q^{61} - 144 q^{64} - 36 q^{69} - 12 q^{70} + 32 q^{71} + 8 q^{74} - 8 q^{75} + 24 q^{79} - 8 q^{80} - 4 q^{81} + 28 q^{84} - 56 q^{86} + 56 q^{89} + 18 q^{90} + 12 q^{94} + 56 q^{95} + 4 q^{96} + 64 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1170, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1170, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1170, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 2}\)