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Properties

Label 805.2.v
Level $805$
Weight $2$
Character orbit 805.v
Rep. character $\chi_{805}(47,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $352$
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.v (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{12})\)
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 400 352 48
Cusp forms 368 352 16
Eisenstein series 32 0 32

Trace form

\( 352 q + 8 q^{7} - 24 q^{8} + O(q^{10}) \) \( 352 q + 8 q^{7} - 24 q^{8} - 24 q^{10} - 8 q^{11} + 8 q^{15} + 160 q^{16} - 36 q^{17} - 16 q^{21} + 16 q^{22} - 36 q^{28} - 16 q^{30} + 12 q^{31} + 64 q^{32} - 12 q^{33} + 12 q^{35} - 288 q^{36} + 12 q^{37} - 36 q^{38} + 72 q^{40} + 72 q^{42} - 60 q^{45} - 72 q^{47} - 144 q^{50} + 24 q^{51} - 52 q^{53} - 56 q^{56} + 40 q^{57} - 16 q^{58} - 40 q^{60} - 48 q^{61} + 36 q^{63} - 28 q^{65} + 144 q^{66} - 8 q^{67} - 12 q^{68} + 112 q^{70} - 88 q^{71} + 100 q^{72} + 48 q^{73} - 48 q^{75} - 40 q^{77} - 24 q^{78} + 160 q^{81} - 32 q^{85} - 40 q^{86} + 60 q^{87} + 28 q^{88} - 80 q^{91} + 32 q^{93} - 24 q^{95} - 168 q^{96} - 108 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
805.2.v.a 805.v 35.k $352$ $6.428$ None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{12}]$

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

\( S_{2}^{\mathrm{old}}(805, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 2}\)