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Properties

Label 1260.2.ch
Level $1260$
Weight $2$
Character orbit 1260.ch
Rep. character $\chi_{1260}(271,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $160$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1260.ch (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 28 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1260, [\chi])\).

Total New Old
Modular forms 608 160 448
Cusp forms 544 160 384
Eisenstein series 64 0 64

Trace form

\( 160 q + 2 q^{2} - 2 q^{4} - 4 q^{8} + O(q^{10}) \) \( 160 q + 2 q^{2} - 2 q^{4} - 4 q^{8} - 18 q^{14} - 6 q^{16} + 24 q^{22} + 80 q^{25} + 30 q^{26} - 22 q^{28} - 24 q^{29} + 22 q^{32} + 24 q^{37} + 60 q^{38} + 26 q^{44} + 10 q^{46} + 32 q^{49} + 4 q^{50} + 36 q^{52} - 8 q^{53} + 64 q^{56} + 10 q^{58} + 24 q^{61} + 4 q^{64} + 4 q^{65} + 20 q^{70} + 72 q^{73} - 46 q^{74} + 24 q^{77} - 102 q^{82} - 8 q^{86} - 52 q^{88} + 60 q^{89} - 36 q^{92} - 126 q^{94} - 78 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1260, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1260, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1260, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)