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Properties

Label 1205.2.q
Level $1205$
Weight $2$
Character orbit 1205.q
Rep. character $\chi_{1205}(249,\cdot)$
Character field $\Q(\zeta_{8})$
Dimension $472$
Sturm bound $242$

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Defining parameters

Level: \( N \) \(=\) \( 1205 = 5 \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1205.q (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1205 \)
Character field: \(\Q(\zeta_{8})\)
Sturm bound: \(242\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1205, [\chi])\).

Total New Old
Modular forms 488 488 0
Cusp forms 472 472 0
Eisenstein series 16 16 0

Trace form

\( 472 q - 4 q^{5} + O(q^{10}) \) \( 472 q - 4 q^{5} - 8 q^{10} - 8 q^{11} - 24 q^{14} - 8 q^{15} - 456 q^{16} + 8 q^{19} + 20 q^{20} - 16 q^{21} + 96 q^{24} + 24 q^{26} + 24 q^{29} - 4 q^{30} + 8 q^{31} - 56 q^{34} - 12 q^{35} - 328 q^{36} - 40 q^{39} + 32 q^{41} - 56 q^{44} + 64 q^{45} - 112 q^{46} - 24 q^{49} - 156 q^{50} - 24 q^{51} + 144 q^{54} + 40 q^{55} + 24 q^{56} + 16 q^{59} - 72 q^{61} + 32 q^{65} - 16 q^{66} - 120 q^{69} + 56 q^{70} - 16 q^{71} + 80 q^{74} + 32 q^{75} - 56 q^{76} + 80 q^{79} + 60 q^{80} - 472 q^{81} + 48 q^{84} - 12 q^{85} - 32 q^{89} + 144 q^{91} + 32 q^{94} + 44 q^{95} + 72 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1205, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.