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Properties

Label 760.2.bf
Level $760$
Weight $2$
Character orbit 760.bf
Rep. character $\chi_{760}(179,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $232$
Newform subspaces $2$
Sturm bound $240$
Trace bound $1$

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Defining parameters

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

Dimensions

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

Total New Old
Modular forms 248 248 0
Cusp forms 232 232 0
Eisenstein series 16 16 0

Trace form

\( 232 q - 4 q^{4} + 4 q^{6} - 112 q^{9} + O(q^{10}) \) \( 232 q - 4 q^{4} + 4 q^{6} - 112 q^{9} + 6 q^{10} - 16 q^{11} - 4 q^{16} - 16 q^{19} - 24 q^{20} + 18 q^{24} - 2 q^{25} - 52 q^{26} - 40 q^{30} + 18 q^{34} - 36 q^{35} - 8 q^{36} + 48 q^{40} - 12 q^{41} - 46 q^{44} + 168 q^{49} - 36 q^{51} - 4 q^{54} - 12 q^{59} + 42 q^{60} - 4 q^{64} + 22 q^{66} + 12 q^{70} - 20 q^{74} - 42 q^{76} - 22 q^{80} - 100 q^{81} + 108 q^{86} - 12 q^{89} - 30 q^{90} - 96 q^{91} + 28 q^{96} + 16 q^{99} + O(q^{100}) \)

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.bf.a 760.bf 760.af $8$ $6.069$ 8.0.207360000.2 \(\Q(\sqrt{-10}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+\beta _{1}q^{2}+(2+2\beta _{4})q^{4}-\beta _{6}q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
760.2.bf.b 760.bf 760.af $224$ $6.069$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$