Properties

Label 76.6.d
Level $76$
Weight $6$
Character orbit 76.d
Rep. character $\chi_{76}(75,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $1$
Sturm bound $60$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 76.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 76 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(60\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(76, [\chi])\).

Total New Old
Modular forms 52 52 0
Cusp forms 48 48 0
Eisenstein series 4 4 0

Trace form

\( 48q - 22q^{4} - 4q^{5} - 246q^{6} + 3516q^{9} + O(q^{10}) \) \( 48q - 22q^{4} - 4q^{5} - 246q^{6} + 3516q^{9} - 1222q^{16} + 1000q^{17} - 300q^{20} + 17158q^{24} + 24996q^{25} + 12102q^{26} + 6382q^{28} - 16528q^{30} + 27524q^{36} + 3598q^{38} + 35966q^{42} - 65408q^{44} - 13476q^{45} - 143096q^{49} - 148446q^{54} - 53980q^{57} - 117018q^{58} + 133740q^{61} + 28068q^{62} - 78130q^{64} + 128204q^{66} - 48338q^{68} - 104080q^{73} + 48932q^{74} - 251688q^{76} + 184844q^{77} + 80080q^{80} + 375128q^{81} + 175628q^{82} - 384748q^{85} + 139810q^{92} + 183272q^{93} + 601258q^{96} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(76, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
76.6.d.a \(48\) \(12.189\) None \(0\) \(0\) \(-4\) \(0\)