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Properties

Label 1859.2.bv
Level $1859$
Weight $2$
Character orbit 1859.bv
Rep. character $\chi_{1859}(2,\cdot)$
Character field $\Q(\zeta_{780})$
Dimension $34560$
Sturm bound $364$

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Defining parameters

Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1859.bv (of order \(780\) and degree \(192\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1859 \)
Character field: \(\Q(\zeta_{780})\)
Sturm bound: \(364\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1859, [\chi])\).

Total New Old
Modular forms 35328 35328 0
Cusp forms 34560 34560 0
Eisenstein series 768 768 0

Trace form

\( 34560 q - 240 q^{2} - 150 q^{3} - 138 q^{4} - 144 q^{5} - 240 q^{6} - 240 q^{7} - 240 q^{8} - 502 q^{9} + O(q^{10}) \) \( 34560 q - 240 q^{2} - 150 q^{3} - 138 q^{4} - 144 q^{5} - 240 q^{6} - 240 q^{7} - 240 q^{8} - 502 q^{9} - 200 q^{11} - 416 q^{12} - 250 q^{13} - 116 q^{14} - 104 q^{15} + 198 q^{16} - 230 q^{17} - 240 q^{18} - 240 q^{19} - 158 q^{20} - 86 q^{22} - 624 q^{23} - 340 q^{24} - 156 q^{25} - 172 q^{26} - 132 q^{27} - 240 q^{28} - 250 q^{29} - 230 q^{30} - 132 q^{31} - 190 q^{33} - 468 q^{34} - 300 q^{35} - 96 q^{36} - 156 q^{37} - 156 q^{38} - 320 q^{39} - 300 q^{40} - 180 q^{41} - 138 q^{42} - 128 q^{44} - 368 q^{45} - 560 q^{46} - 146 q^{47} - 182 q^{48} - 138 q^{49} - 290 q^{50} - 260 q^{51} + 360 q^{52} - 120 q^{53} - 418 q^{55} - 488 q^{56} - 240 q^{57} - 268 q^{58} - 236 q^{59} - 820 q^{60} - 250 q^{61} - 230 q^{62} - 290 q^{63} - 156 q^{64} - 114 q^{66} + 316 q^{67} - 250 q^{68} - 372 q^{69} - 442 q^{70} - 256 q^{71} - 240 q^{72} - 270 q^{73} - 250 q^{74} - 482 q^{75} - 208 q^{77} - 764 q^{78} - 140 q^{79} - 148 q^{80} - 486 q^{81} + 510 q^{82} - 430 q^{83} - 220 q^{84} - 200 q^{85} + 176 q^{86} - 330 q^{88} - 508 q^{89} - 260 q^{90} - 100 q^{91} - 364 q^{92} + 108 q^{93} - 350 q^{94} - 530 q^{95} - 630 q^{96} + 326 q^{97} - 72 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1859, [\chi])\) into newform subspaces

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