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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

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

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

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