↑

Properties

Label 2310.2.bc
Level $2310$
Weight $2$
Character orbit 2310.bc
Rep. character $\chi_{2310}(551,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $208$
Sturm bound $1152$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 2310 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2310.bc (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 1184 208 976
Cusp forms 1120 208 912
Eisenstein series 64 0 64

Trace form

\( 208 q + 104 q^{4} - 32 q^{7} - 4 q^{9} + O(q^{10}) \) \( 208 q + 104 q^{4} - 32 q^{7} - 4 q^{9} - 104 q^{16} - 4 q^{21} + 12 q^{24} - 104 q^{25} - 16 q^{28} + 4 q^{30} - 48 q^{31} - 8 q^{36} + 24 q^{37} + 24 q^{39} - 24 q^{42} - 12 q^{45} - 8 q^{46} + 72 q^{49} - 32 q^{51} + 48 q^{52} + 72 q^{54} + 64 q^{57} - 24 q^{58} + 120 q^{61} + 24 q^{63} - 208 q^{64} + 16 q^{67} - 24 q^{70} - 32 q^{78} - 16 q^{79} + 20 q^{81} - 8 q^{84} - 48 q^{91} + 48 q^{93} + 12 q^{96} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2310, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(462, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1155, [\chi])\)\(^{\oplus 2}\)