Properties

Label 1210.2.f
Level $1210$
Weight $2$
Character orbit 1210.f
Rep. character $\chi_{1210}(483,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $108$
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.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(i)\)
Sturm bound: \(396\)

Dimensions

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

Total New Old
Modular forms 444 108 336
Cusp forms 348 108 240
Eisenstein series 96 0 96

Trace form

\( 108q - 8q^{3} - 8q^{5} + O(q^{10}) \) \( 108q - 8q^{3} - 8q^{5} + 8q^{12} - 108q^{16} - 8q^{20} + 16q^{23} + 32q^{25} + 8q^{26} + 16q^{27} + 16q^{31} - 124q^{36} + 32q^{37} + 24q^{38} - 40q^{42} - 56q^{45} - 24q^{47} + 8q^{48} - 56q^{53} - 8q^{56} - 32q^{58} - 24q^{60} + 24q^{67} - 32q^{70} - 96q^{71} + 72q^{75} + 16q^{78} + 8q^{80} - 188q^{81} - 16q^{82} + 64q^{86} + 32q^{91} - 16q^{92} + 56q^{93} + 24q^{97} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1210, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(605, [\chi])\)\(^{\oplus 2}\)