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Properties

Label 805.2.k
Level $805$
Weight $2$
Character orbit 805.k
Rep. character $\chi_{805}(622,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $176$
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.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(i)\)
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 200 176 24
Cusp forms 184 176 8
Eisenstein series 16 0 16

Trace form

\( 176 q - 8 q^{7} + 24 q^{8} + O(q^{10}) \) \( 176 q - 8 q^{7} + 24 q^{8} + 8 q^{11} - 8 q^{15} - 208 q^{16} + 16 q^{21} - 16 q^{22} + 36 q^{28} + 88 q^{30} + 8 q^{32} - 48 q^{35} - 144 q^{36} + 24 q^{37} + 24 q^{50} - 24 q^{51} - 8 q^{53} + 104 q^{56} - 40 q^{57} - 80 q^{58} + 40 q^{60} + 60 q^{63} - 8 q^{65} - 64 q^{67} + 68 q^{70} + 40 q^{71} + 80 q^{72} + 4 q^{77} + 168 q^{78} - 160 q^{81} - 16 q^{85} - 128 q^{86} - 88 q^{88} - 112 q^{91} - 32 q^{93} + 24 q^{98} + O(q^{100}) \)

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.k.a 805.k 35.f $176$ $6.428$ None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$

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

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