Properties

Label 76.2.f
Level $76$
Weight $2$
Character orbit 76.f
Rep. character $\chi_{76}(27,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
Newform subspaces $1$
Sturm bound $20$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 76.f (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 76 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(20\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(76, [\chi])\).

Total New Old
Modular forms 24 24 0
Cusp forms 16 16 0
Eisenstein series 8 8 0

Trace form

\( 16 q - 3 q^{2} - 3 q^{4} - 2 q^{5} + 5 q^{6} - 4 q^{9} + O(q^{10}) \) \( 16 q - 3 q^{2} - 3 q^{4} - 2 q^{5} + 5 q^{6} - 4 q^{9} - 6 q^{10} - 18 q^{13} - 6 q^{14} - 3 q^{16} + 2 q^{17} + 4 q^{20} + 3 q^{22} - 23 q^{24} - 2 q^{25} - 24 q^{26} - 4 q^{28} - 6 q^{29} + 28 q^{30} + 27 q^{32} + 18 q^{33} + 36 q^{34} + 14 q^{36} - 24 q^{38} + 48 q^{40} - 48 q^{41} + 28 q^{42} - 25 q^{44} + 24 q^{45} + 9 q^{48} + 16 q^{49} + 6 q^{52} + 6 q^{53} + 17 q^{54} - 26 q^{57} - 40 q^{58} - 6 q^{60} - 26 q^{61} + 32 q^{62} - 18 q^{64} + 5 q^{66} - 36 q^{68} - 54 q^{70} - 66 q^{72} + 16 q^{73} - 2 q^{74} + 43 q^{76} + 80 q^{77} - 84 q^{78} - 30 q^{80} + 12 q^{81} + 11 q^{82} + 14 q^{85} - 48 q^{86} + 18 q^{89} - 18 q^{90} - 52 q^{92} - 20 q^{93} + 46 q^{96} - 12 q^{97} + 51 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(76, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
76.2.f.a 76.f 76.f $16$ $0.607$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-3\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{1}-\beta _{14})q^{2}+\beta _{15}q^{3}+(-1+\cdots)q^{4}+\cdots\)