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Properties

Label 2310.2.u
Level $2310$
Weight $2$
Character orbit 2310.u
Rep. character $\chi_{2310}(617,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $240$
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.u (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q(i)\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 1184 240 944
Cusp forms 1120 240 880
Eisenstein series 64 0 64

Trace form

\( 240 q - 8 q^{3} + O(q^{10}) \) \( 240 q - 8 q^{3} + 8 q^{12} - 32 q^{13} - 8 q^{15} - 240 q^{16} + 16 q^{18} - 48 q^{25} - 8 q^{27} + 8 q^{33} + 16 q^{37} + 32 q^{40} + 80 q^{45} + 8 q^{48} + 64 q^{51} + 32 q^{52} + 48 q^{55} - 64 q^{57} + 32 q^{58} - 8 q^{60} - 16 q^{63} - 48 q^{67} - 16 q^{72} + 96 q^{73} - 72 q^{75} - 16 q^{78} + 16 q^{81} - 128 q^{82} + 96 q^{85} + 160 q^{87} - 80 q^{90} + 80 q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2310, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(330, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1155, [\chi])\)\(^{\oplus 2}\)