Properties

Label 760.2.co
Level $760$
Weight $2$
Character orbit 760.co
Rep. character $\chi_{760}(33,\cdot)$
Character field $\Q(\zeta_{36})$
Dimension $360$
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.co (of order \(36\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 95 \)
Character field: \(\Q(\zeta_{36})\)
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 1536 360 1176
Cusp forms 1344 360 984
Eisenstein series 192 0 192

Trace form

\( 360 q + O(q^{10}) \) \( 360 q + 24 q^{23} + 24 q^{25} + 72 q^{33} - 36 q^{41} + 48 q^{43} + 24 q^{47} - 72 q^{51} + 72 q^{55} - 24 q^{57} + 108 q^{63} - 144 q^{67} - 72 q^{77} - 48 q^{81} - 36 q^{83} - 72 q^{87} + 72 q^{91} + 36 q^{93} + O(q^{100}) \)

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.co.a 760.co 95.r $360$ $6.069$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{36}]$

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

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