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Properties

Label 2365.2.dk
Level $2365$
Weight $2$
Character orbit 2365.dk
Rep. character $\chi_{2365}(9,\cdot)$
Character field $\Q(\zeta_{210})$
Dimension $12480$
Sturm bound $528$

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Defining parameters

Level: \( N \) \(=\) \( 2365 = 5 \cdot 11 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2365.dk (of order \(210\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 2365 \)
Character field: \(\Q(\zeta_{210})\)
Sturm bound: \(528\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2365, [\chi])\).

Total New Old
Modular forms 12864 12864 0
Cusp forms 12480 12480 0
Eisenstein series 384 384 0

Trace form

\( 12480 q - 572 q^{4} - 35 q^{5} - 28 q^{6} + 174 q^{9} + O(q^{10}) \) \( 12480 q - 572 q^{4} - 35 q^{5} - 28 q^{6} + 174 q^{9} - 108 q^{10} - 84 q^{11} - 10 q^{14} - 19 q^{15} + 496 q^{16} - 70 q^{19} - 69 q^{20} - 100 q^{21} - 206 q^{24} - 41 q^{25} - 62 q^{26} - 54 q^{29} - 73 q^{30} - 86 q^{31} - 208 q^{34} + 78 q^{35} + 1432 q^{36} - 244 q^{39} - 226 q^{40} - 60 q^{41} - 820 q^{44} - 132 q^{45} - 58 q^{46} - 1422 q^{49} - 23 q^{50} - 140 q^{51} - 72 q^{54} - 15 q^{55} + 132 q^{56} - 40 q^{59} + 89 q^{60} - 150 q^{61} - 316 q^{64} - 124 q^{65} - 276 q^{66} - 150 q^{69} - 27 q^{70} - 70 q^{71} - 268 q^{74} - 88 q^{75} + 200 q^{76} - 48 q^{79} - 112 q^{80} - 310 q^{81} - 342 q^{84} - 240 q^{85} - 104 q^{86} - 472 q^{89} - 104 q^{90} + 54 q^{91} - 416 q^{94} - 15 q^{95} - 386 q^{96} - 546 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2365, [\chi])\) into newform subspaces

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