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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

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

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

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