Properties

Label 1210.2.j
Level $1210$
Weight $2$
Character orbit 1210.j
Rep. character $\chi_{1210}(9,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $216$
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.j (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(396\)

Dimensions

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

Total New Old
Modular forms 888 216 672
Cusp forms 696 216 480
Eisenstein series 192 0 192

Trace form

\( 216q + 54q^{4} - 4q^{6} + 74q^{9} + O(q^{10}) \) \( 216q + 54q^{4} - 4q^{6} + 74q^{9} + 4q^{10} + 6q^{14} - 14q^{15} - 54q^{16} + 16q^{19} + 40q^{21} + 4q^{24} + 12q^{25} + 4q^{26} + 4q^{29} + 26q^{30} - 4q^{31} - 8q^{34} + 52q^{35} - 54q^{36} + 36q^{39} + 6q^{40} - 46q^{41} - 52q^{45} - 32q^{46} - 8q^{49} + 4q^{50} - 12q^{51} - 64q^{54} + 4q^{56} + 4q^{59} - 16q^{60} - 56q^{61} + 54q^{64} - 44q^{65} - 48q^{69} - 16q^{70} + 80q^{71} - 56q^{75} + 4q^{76} + 4q^{79} - 10q^{80} + 86q^{81} + 20q^{84} + 38q^{85} + 8q^{86} + 188q^{89} - 10q^{90} - 2q^{91} + 30q^{94} + 50q^{95} - 4q^{96} + O(q^{100}) \)

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

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