Properties

Label 805.2.bb
Level $805$
Weight $2$
Character orbit 805.bb
Rep. character $\chi_{805}(76,\cdot)$
Character field $\Q(\zeta_{22})$
Dimension $640$
Newform subspaces $2$
Sturm bound $192$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 805 = 5 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 805.bb (of order \(22\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 161 \)
Character field: \(\Q(\zeta_{22})\)
Newform subspaces: \( 2 \)
Sturm bound: \(192\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 1000 640 360
Cusp forms 920 640 280
Eisenstein series 80 0 80

Trace form

\( 640 q + 4 q^{2} - 68 q^{4} + 12 q^{8} + 56 q^{9} + O(q^{10}) \) \( 640 q + 4 q^{2} - 68 q^{4} + 12 q^{8} + 56 q^{9} - 48 q^{16} + 12 q^{18} - 66 q^{21} - 16 q^{23} - 64 q^{25} + 12 q^{29} + 24 q^{32} + 16 q^{35} + 30 q^{36} - 48 q^{39} - 88 q^{43} - 22 q^{44} + 32 q^{46} + 64 q^{49} - 18 q^{50} - 88 q^{51} + 176 q^{56} - 246 q^{58} + 110 q^{63} - 124 q^{64} + 12 q^{70} - 20 q^{71} - 436 q^{72} + 22 q^{74} + 138 q^{77} - 400 q^{78} - 88 q^{79} - 144 q^{81} + 66 q^{84} - 4 q^{85} - 44 q^{86} + 330 q^{88} - 516 q^{92} - 88 q^{93} + 16 q^{95} + 124 q^{98} - 528 q^{99} + O(q^{100}) \)

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.bb.a 805.bb 161.k $320$ $6.428$ None \(2\) \(0\) \(-32\) \(-3\) $\mathrm{SU}(2)[C_{22}]$
805.2.bb.b 805.bb 161.k $320$ $6.428$ None \(2\) \(0\) \(32\) \(3\) $\mathrm{SU}(2)[C_{22}]$

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

\( S_{2}^{\mathrm{old}}(805, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 2}\)