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Properties

Label 1170.2.cf
Level $1170$
Weight $2$
Character orbit 1170.cf
Rep. character $\chi_{1170}(37,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $140$
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.cf (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 65 \)
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 1072 140 932
Cusp forms 944 140 804
Eisenstein series 128 0 128

Trace form

\( 140 q + 70 q^{4} - 2 q^{5} + O(q^{10}) \) \( 140 q + 70 q^{4} - 2 q^{5} - 4 q^{11} + 18 q^{13} - 70 q^{16} - 4 q^{17} - 28 q^{19} + 2 q^{20} - 16 q^{23} - 18 q^{25} + 24 q^{31} + 6 q^{34} + 12 q^{35} - 24 q^{37} + 38 q^{41} + 16 q^{43} - 20 q^{44} + 20 q^{46} - 16 q^{47} - 90 q^{49} - 8 q^{50} + 12 q^{52} - 6 q^{53} + 56 q^{55} + 12 q^{56} + 10 q^{58} + 36 q^{59} - 8 q^{61} + 48 q^{62} - 140 q^{64} - 32 q^{65} + 72 q^{67} - 2 q^{68} + 56 q^{70} + 8 q^{71} + 30 q^{74} - 8 q^{76} - 40 q^{77} + 4 q^{80} + 38 q^{82} + 160 q^{83} - 2 q^{85} - 18 q^{89} - 32 q^{92} - 24 q^{94} + 24 q^{95} + 36 q^{97} - 48 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1170, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 2}\)