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Properties

Label 2310.2.cf
Level $2310$
Weight $2$
Character orbit 2310.cf
Rep. character $\chi_{2310}(397,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $320$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 2310 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2310.cf (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2310, [\chi])\).

Total New Old
Modular forms 2368 320 2048
Cusp forms 2240 320 1920
Eisenstein series 128 0 128

Trace form

\( 320 q + O(q^{10}) \) \( 320 q + 160 q^{16} - 32 q^{21} + 32 q^{23} + 96 q^{31} - 320 q^{36} + 96 q^{38} + 128 q^{43} - 32 q^{53} - 64 q^{58} - 96 q^{61} + 16 q^{67} + 16 q^{70} + 128 q^{71} + 96 q^{73} + 48 q^{75} + 64 q^{78} + 160 q^{81} - 48 q^{82} + 96 q^{85} + 32 q^{86} - 144 q^{87} - 96 q^{91} - 64 q^{92} + 32 q^{95} + 32 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2310, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2310, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2310, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)