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Properties

Label 760.2.cg
Level $760$
Weight $2$
Character orbit 760.cg
Rep. character $\chi_{760}(9,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $180$
Newform subspaces $1$
Sturm bound $240$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 760.cg (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(240\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(760, [\chi])\).

Total New Old
Modular forms 768 180 588
Cusp forms 672 180 492
Eisenstein series 96 0 96

Trace form

\( 180 q + O(q^{10}) \) \( 180 q - 12 q^{15} + 12 q^{25} + 24 q^{35} - 18 q^{41} + 18 q^{45} + 90 q^{49} + 36 q^{51} - 36 q^{55} - 12 q^{59} + 48 q^{69} - 24 q^{71} - 156 q^{79} + 24 q^{81} + 12 q^{85} - 36 q^{89} + 36 q^{91} + 78 q^{95} + 42 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(760, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
760.2.cg.a 760.cg 95.p $180$ $6.069$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{2}^{\mathrm{old}}(760, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(760, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 2}\)