Properties

Label 805.2.be
Level $805$
Weight $2$
Character orbit 805.be
Rep. character $\chi_{805}(29,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $720$
Newform subspaces $1$
Sturm bound $192$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 805 = 5 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 805.be (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 115 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 1 \)
Sturm bound: \(192\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(805, [\chi])\).

Total New Old
Modular forms 1000 720 280
Cusp forms 920 720 200
Eisenstein series 80 0 80

Trace form

\( 720q + 80q^{4} + 4q^{5} - 8q^{6} + 64q^{9} + O(q^{10}) \) \( 720q + 80q^{4} + 4q^{5} - 8q^{6} + 64q^{9} + 16q^{11} - 8q^{14} - 18q^{15} - 96q^{16} - 36q^{20} + 8q^{21} + 24q^{24} - 30q^{25} + 40q^{26} - 8q^{29} - 44q^{30} - 8q^{31} + 12q^{34} + 4q^{35} - 72q^{36} - 72q^{39} - 20q^{40} - 16q^{41} - 148q^{44} + 32q^{45} - 32q^{46} + 72q^{49} + 32q^{50} - 248q^{54} - 88q^{55} - 72q^{59} - 200q^{60} - 40q^{61} - 20q^{65} + 128q^{66} - 208q^{69} - 8q^{70} + 188q^{71} - 128q^{74} + 132q^{75} - 44q^{76} - 40q^{79} - 180q^{80} - 264q^{81} - 24q^{84} - 4q^{85} - 376q^{86} + 48q^{89} + 394q^{90} - 160q^{91} + 144q^{94} + 64q^{95} - 732q^{96} - 88q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(805, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
805.2.be.a \(720\) \(6.428\) None \(0\) \(0\) \(4\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(805, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(805, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 2}\)