Properties

Label 1210.2.o
Level $1210$
Weight $2$
Character orbit 1210.o
Rep. character $\chi_{1210}(89,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $660$
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.o (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 605 \)
Character field: \(\Q(\zeta_{22})\)
Sturm bound: \(396\)

Dimensions

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

Total New Old
Modular forms 2020 660 1360
Cusp forms 1940 660 1280
Eisenstein series 80 0 80

Trace form

\( 660q + 66q^{4} - 4q^{5} + 4q^{6} - 652q^{9} + O(q^{10}) \) \( 660q + 66q^{4} - 4q^{5} + 4q^{6} - 652q^{9} + 18q^{10} - 46q^{11} + 4q^{14} + 4q^{15} - 66q^{16} - 16q^{19} + 4q^{20} - 4q^{24} - 4q^{26} - 4q^{29} + 4q^{30} + 8q^{34} + 8q^{35} - 74q^{36} - 16q^{39} + 4q^{40} + 36q^{41} + 2q^{44} + 36q^{45} + 12q^{46} - 50q^{49} - 24q^{50} + 128q^{51} - 16q^{54} + 50q^{55} - 4q^{56} + 4q^{59} - 4q^{60} + 36q^{61} + 66q^{64} - 82q^{65} - 8q^{66} + 16q^{69} + 36q^{70} - 48q^{71} - 8q^{75} + 38q^{76} - 72q^{79} - 4q^{80} + 676q^{81} + 80q^{85} - 8q^{86} + 192q^{89} - 68q^{90} + 92q^{91} + 108q^{94} - 176q^{95} + 4q^{96} + 206q^{99} + O(q^{100}) \)

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

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