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Properties

Label 2310.2.bp
Level $2310$
Weight $2$
Character orbit 2310.bp
Rep. character $\chi_{2310}(391,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $256$
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.bp (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 2368 256 2112
Cusp forms 2240 256 1984
Eisenstein series 128 0 128

Trace form

\( 256 q + 64 q^{4} + 64 q^{9} + O(q^{10}) \) \( 256 q + 64 q^{4} + 64 q^{9} - 8 q^{11} - 4 q^{14} - 64 q^{16} + 16 q^{22} + 64 q^{25} - 80 q^{29} - 64 q^{36} - 16 q^{37} + 8 q^{42} + 8 q^{44} - 36 q^{49} - 80 q^{51} + 24 q^{56} - 16 q^{58} + 64 q^{64} + 128 q^{67} + 96 q^{71} + 160 q^{74} + 128 q^{77} + 240 q^{79} - 64 q^{81} + 64 q^{88} + 76 q^{91} + 64 q^{93} + 8 q^{99} + O(q^{100}) \)

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

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