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Properties

Label 2310.2.f
Level $2310$
Weight $2$
Character orbit 2310.f
Rep. character $\chi_{2310}(881,\cdot)$
Character field $\Q$
Dimension $112$
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.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 592 112 480
Cusp forms 560 112 448
Eisenstein series 32 0 32

Trace form

\( 112 q - 112 q^{4} - 24 q^{7} - 8 q^{9} + O(q^{10}) \) \( 112 q - 112 q^{4} - 24 q^{7} - 8 q^{9} + 112 q^{16} - 8 q^{21} + 112 q^{25} + 24 q^{28} + 8 q^{30} + 8 q^{36} - 64 q^{37} + 48 q^{39} + 24 q^{42} - 64 q^{43} - 64 q^{46} + 8 q^{49} + 32 q^{51} + 32 q^{57} - 24 q^{63} - 112 q^{64} + 192 q^{67} + 24 q^{70} - 16 q^{78} + 80 q^{79} - 8 q^{81} + 8 q^{84} + 48 q^{91} - 48 q^{93} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2310, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(462, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1155, [\chi])\)\(^{\oplus 2}\)