Properties

Label 760.2.d
Level $760$
Weight $2$
Character orbit 760.d
Rep. character $\chi_{760}(609,\cdot)$
Character field $\Q$
Dimension $26$
Newform subspaces $5$
Sturm bound $240$
Trace bound $5$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 128 26 102
Cusp forms 112 26 86
Eisenstein series 16 0 16

Trace form

\( 26 q + 4 q^{5} - 26 q^{9} + O(q^{10}) \) \( 26 q + 4 q^{5} - 26 q^{9} + 12 q^{11} - 8 q^{15} - 6 q^{19} - 8 q^{21} + 4 q^{25} - 4 q^{29} + 18 q^{35} + 16 q^{39} + 20 q^{41} - 8 q^{45} - 54 q^{49} - 48 q^{51} - 6 q^{55} + 40 q^{61} + 4 q^{65} - 16 q^{69} - 24 q^{71} - 4 q^{75} + 24 q^{79} + 10 q^{81} - 10 q^{85} - 12 q^{89} - 32 q^{91} + 28 q^{99} + O(q^{100}) \)

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.d.a 760.d 5.b $2$ $6.069$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(-1+i)q^{5}+iq^{7}-q^{9}+\cdots\)
760.2.d.b 760.d 5.b $4$ $6.069$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-1+\beta _{2})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
760.2.d.c 760.d 5.b $4$ $6.069$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(\zeta_{8}-2\zeta_{8}^{3})q^{5}+\cdots\)
760.2.d.d 760.d 5.b $4$ $6.069$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}^{2}q^{3}+(1+\zeta_{8})q^{5}+(-\zeta_{8}-2\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
760.2.d.e 760.d 5.b $12$ $6.069$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{11}q^{3}-\beta _{1}q^{5}+(\beta _{5}+\beta _{11})q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(760, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(380, [\chi])\)\(^{\oplus 2}\)