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Properties

Label 805.2.s
Level $805$
Weight $2$
Character orbit 805.s
Rep. character $\chi_{805}(254,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $176$
Newform subspaces $4$
Sturm bound $192$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 805 = 5 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 805.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 35 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(192\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

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

\( 176 q + 88 q^{4} - 16 q^{6} + 92 q^{9} + O(q^{10}) \) \( 176 q + 88 q^{4} - 16 q^{6} + 92 q^{9} - 2 q^{10} - 4 q^{11} - 28 q^{14} - 20 q^{15} - 80 q^{16} - 8 q^{19} - 24 q^{20} + 4 q^{21} - 24 q^{24} - 12 q^{25} + 8 q^{26} - 4 q^{29} - 8 q^{30} + 2 q^{31} + 16 q^{34} + 28 q^{35} + 128 q^{36} + 32 q^{39} - 32 q^{41} + 8 q^{44} + 42 q^{45} - 14 q^{49} - 12 q^{50} - 44 q^{51} - 60 q^{54} + 36 q^{55} - 4 q^{56} - 66 q^{59} - 32 q^{60} + 8 q^{61} - 24 q^{64} + 14 q^{65} - 64 q^{66} + 32 q^{69} + 54 q^{70} + 4 q^{71} - 8 q^{74} - 50 q^{75} + 152 q^{76} + 20 q^{79} - 24 q^{80} - 120 q^{81} - 208 q^{84} + 76 q^{86} + 20 q^{89} - 140 q^{90} + 16 q^{91} - 40 q^{94} - 12 q^{95} + 12 q^{96} + 32 q^{99} + O(q^{100}) \)

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.s.a 805.s 35.j $4$ $6.428$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-2\zeta_{12}q^{3}+(-2+2\zeta_{12}^{2})q^{4}+(\zeta_{12}+\cdots)q^{5}+\cdots\)
805.2.s.b 805.s 35.j $4$ $6.428$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+(2\zeta_{12}-2\zeta_{12}^{3})q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
805.2.s.c 805.s 35.j $4$ $6.428$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+2\zeta_{12}q^{2}+(-2\zeta_{12}+2\zeta_{12}^{3})q^{3}+\cdots\)
805.2.s.d 805.s 35.j $164$ $6.428$ None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{6}]$

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

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