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Properties

Label 2310.2.db
Level $2310$
Weight $2$
Character orbit 2310.db
Rep. character $\chi_{2310}(61,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $512$
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.db (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
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 512 4224
Cusp forms 4480 512 3968
Eisenstein series 256 0 256

Trace form

\( 512 q - 64 q^{4} - 64 q^{9} + O(q^{10}) \) \( 512 q - 64 q^{4} - 64 q^{9} - 4 q^{11} + 4 q^{14} + 64 q^{16} - 120 q^{17} - 16 q^{22} - 64 q^{25} + 24 q^{26} + 80 q^{29} - 128 q^{36} - 8 q^{37} - 48 q^{38} + 16 q^{42} + 4 q^{44} - 48 q^{47} - 72 q^{49} - 40 q^{51} - 8 q^{58} + 128 q^{64} + 64 q^{67} + 120 q^{68} - 96 q^{71} + 360 q^{73} + 80 q^{74} + 160 q^{77} + 120 q^{79} + 64 q^{81} + 144 q^{82} + 32 q^{88} + 96 q^{89} + 68 q^{91} + 32 q^{93} + 60 q^{94} - 8 q^{99} + O(q^{100}) \)

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

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