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Properties

Label 1805.2.bf
Level $1805$
Weight $2$
Character orbit 1805.bf
Rep. character $\chi_{1805}(4,\cdot)$
Character field $\Q(\zeta_{342})$
Dimension $20304$
Sturm bound $380$

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Defining parameters

Level: \( N \) \(=\) \( 1805 = 5 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1805.bf (of order \(342\) and degree \(108\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1805 \)
Character field: \(\Q(\zeta_{342})\)
Sturm bound: \(380\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1805, [\chi])\).

Total New Old
Modular forms 20736 20736 0
Cusp forms 20304 20304 0
Eisenstein series 432 432 0

Trace form

\( 20304 q - 210 q^{4} - 108 q^{5} - 222 q^{6} - 216 q^{9} + O(q^{10}) \) \( 20304 q - 210 q^{4} - 108 q^{5} - 222 q^{6} - 216 q^{9} - 99 q^{10} - 222 q^{11} - 234 q^{14} - 117 q^{15} - 186 q^{16} - 240 q^{19} - 132 q^{20} - 174 q^{21} - 252 q^{24} - 126 q^{25} - 216 q^{26} - 228 q^{29} - 132 q^{30} - 186 q^{31} - 192 q^{34} - 120 q^{35} - 246 q^{36} - 180 q^{39} - 180 q^{40} - 234 q^{41} - 222 q^{44} - 120 q^{45} - 222 q^{46} - 750 q^{49} - 96 q^{50} - 336 q^{51} - 252 q^{54} - 114 q^{55} - 264 q^{56} - 192 q^{59} - 276 q^{61} - 768 q^{64} - 96 q^{65} - 408 q^{66} + 732 q^{69} - 447 q^{70} - 204 q^{71} - 426 q^{74} - 186 q^{75} - 294 q^{76} - 276 q^{79} - 75 q^{80} - 150 q^{81} - 174 q^{84} - 30 q^{85} + 840 q^{86} - 216 q^{89} - 132 q^{90} - 84 q^{91} - 156 q^{94} + 177 q^{95} - 132 q^{96} - 192 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1805, [\chi])\) into newform subspaces

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