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Properties

Label 1210.2.q
Level $1210$
Weight $2$
Character orbit 1210.q
Rep. character $\chi_{1210}(43,\cdot)$
Character field $\Q(\zeta_{44})$
Dimension $1320$
Sturm bound $396$

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Defining parameters

Level: \( N \) \(=\) \( 1210 = 2 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1210.q (of order \(44\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 605 \)
Character field: \(\Q(\zeta_{44})\)
Sturm bound: \(396\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1210, [\chi])\).

Total New Old
Modular forms 4040 1320 2720
Cusp forms 3880 1320 2560
Eisenstein series 160 0 160

Trace form

\( 1320 q - 8 q^{5} + O(q^{10}) \) \( 1320 q - 8 q^{5} + 44 q^{10} + 12 q^{11} + 88 q^{13} + 8 q^{15} + 132 q^{16} + 84 q^{22} + 8 q^{23} + 8 q^{25} + 8 q^{26} + 16 q^{31} - 4 q^{33} + 116 q^{36} - 124 q^{37} - 108 q^{38} - 40 q^{42} - 32 q^{45} - 16 q^{47} + 352 q^{51} - 64 q^{53} - 72 q^{55} - 8 q^{56} - 32 q^{58} - 16 q^{60} + 220 q^{63} - 16 q^{66} + 192 q^{67} + 88 q^{70} - 16 q^{71} + 96 q^{75} - 44 q^{76} - 16 q^{77} + 16 q^{78} + 8 q^{80} - 1320 q^{81} + 16 q^{82} + 176 q^{85} + 64 q^{86} - 4 q^{88} - 232 q^{91} + 36 q^{92} + 56 q^{93} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1210, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1210, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1210, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(605, [\chi])\)\(^{\oplus 2}\)