Properties

Label 76.5.c
Level $76$
Weight $5$
Character orbit 76.c
Rep. character $\chi_{76}(37,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $2$
Sturm bound $50$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 76.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(50\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(76, [\chi])\).

Total New Old
Modular forms 43 6 37
Cusp forms 37 6 31
Eisenstein series 6 0 6

Trace form

\( 6q - 9q^{5} + 97q^{7} - 52q^{9} + O(q^{10}) \) \( 6q - 9q^{5} + 97q^{7} - 52q^{9} + 39q^{11} - 723q^{17} + 68q^{19} + 774q^{23} + 1153q^{25} - 861q^{35} - 2262q^{39} + 579q^{43} - 5681q^{45} + 4047q^{47} + 2787q^{49} - 6533q^{55} + 5490q^{57} + 2911q^{61} + 643q^{63} + 177q^{73} + 17739q^{77} - 17014q^{81} - 7488q^{83} - 401q^{85} - 14526q^{87} - 1284q^{93} - 837q^{95} + 27259q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(76, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
76.5.c.a \(2\) \(7.856\) \(\Q(\sqrt{57}) \) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(-31\) \(73\) \(q+(-17-3\beta )q^{5}+(39+5\beta )q^{7}+3^{4}q^{9}+\cdots\)
76.5.c.b \(4\) \(7.856\) \(\mathbb{Q}[x]/(x^{4} + \cdots)\) None \(0\) \(0\) \(22\) \(24\) \(q+\beta _{1}q^{3}+(6-\beta _{2})q^{5}+(7-2\beta _{2})q^{7}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(76, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(76, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 2}\)