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Properties

Label 1170.2.dg
Level $1170$
Weight $2$
Character orbit 1170.dg
Rep. character $\chi_{1170}(443,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $288$
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.dg (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 45 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(504\)

Dimensions

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

Total New Old
Modular forms 1040 288 752
Cusp forms 976 288 688
Eisenstein series 64 0 64

Trace form

\( 288 q - 8 q^{3} + 16 q^{6} + O(q^{10}) \) \( 288 q - 8 q^{3} + 16 q^{6} + 8 q^{12} + 16 q^{15} + 144 q^{16} + 24 q^{20} + 24 q^{25} + 4 q^{27} + 24 q^{30} - 16 q^{33} - 16 q^{36} + 48 q^{37} + 24 q^{41} - 76 q^{42} - 56 q^{45} + 48 q^{46} + 24 q^{47} - 16 q^{48} - 96 q^{50} + 96 q^{51} + 48 q^{55} - 24 q^{56} - 80 q^{57} - 24 q^{58} + 8 q^{60} + 24 q^{61} + 24 q^{63} + 32 q^{66} + 24 q^{67} + 72 q^{68} + 16 q^{75} + 40 q^{81} + 144 q^{86} + 8 q^{87} + 4 q^{90} - 136 q^{93} - 120 q^{95} + 8 q^{96} + 24 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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