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Properties

Label 2310.2.dg
Level $2310$
Weight $2$
Character orbit 2310.dg
Rep. character $\chi_{2310}(431,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1024$
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.dg (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 231 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 4736 1024 3712
Cusp forms 4480 1024 3456
Eisenstein series 256 0 256

Trace form

\( 1024 q + 128 q^{4} - 12 q^{9} + O(q^{10}) \) \( 1024 q + 128 q^{4} - 12 q^{9} + 24 q^{15} + 128 q^{16} - 128 q^{25} + 72 q^{27} + 32 q^{33} + 64 q^{34} - 16 q^{36} + 8 q^{37} - 20 q^{39} + 24 q^{42} - 16 q^{49} - 20 q^{51} - 16 q^{55} - 8 q^{58} + 8 q^{60} - 80 q^{61} + 200 q^{63} - 256 q^{64} + 32 q^{66} + 272 q^{69} + 40 q^{72} + 64 q^{78} + 4 q^{81} + 16 q^{82} + 80 q^{84} + 36 q^{93} - 80 q^{94} + 48 q^{97} + 208 q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2310, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(462, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1155, [\chi])\)\(^{\oplus 2}\)