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Properties

Label 2310.2.q
Level $2310$
Weight $2$
Character orbit 2310.q
Rep. character $\chi_{2310}(331,\cdot)$
Character field $\Q(\zeta_{3})$
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.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 1184 112 1072
Cusp forms 1120 112 1008
Eisenstein series 64 0 64

Trace form

\( 112 q - 56 q^{4} - 56 q^{9} + O(q^{10}) \) \( 112 q - 56 q^{4} - 56 q^{9} - 56 q^{16} - 56 q^{25} + 32 q^{29} - 16 q^{31} + 8 q^{33} + 16 q^{34} + 16 q^{35} + 112 q^{36} + 24 q^{37} + 32 q^{39} - 64 q^{41} - 16 q^{42} - 96 q^{43} + 16 q^{46} - 16 q^{47} + 16 q^{49} + 16 q^{51} - 16 q^{53} - 64 q^{57} + 8 q^{58} + 16 q^{59} + 112 q^{64} + 32 q^{67} + 16 q^{69} + 16 q^{74} + 16 q^{77} - 32 q^{78} + 48 q^{79} - 56 q^{81} + 48 q^{82} + 64 q^{83} + 32 q^{85} - 16 q^{86} - 48 q^{89} - 32 q^{91} + 32 q^{93} - 16 q^{95} - 48 q^{97} - 32 q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2310, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(385, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(462, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(770, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1155, [\chi])\)\(^{\oplus 2}\)