Properties

Label 76.8.a
Level $76$
Weight $8$
Character orbit 76.a
Rep. character $\chi_{76}(1,\cdot)$
Character field $\Q$
Dimension $11$
Newform subspaces $2$
Sturm bound $80$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 76.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(80\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(76))\).

Total New Old
Modular forms 73 11 62
Cusp forms 67 11 56
Eisenstein series 6 0 6

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(19\)FrickeDim.
\(-\)\(+\)\(-\)\(5\)
\(-\)\(-\)\(+\)\(6\)
Plus space\(+\)\(6\)
Minus space\(-\)\(5\)

Trace form

\( 11q + 26q^{3} - q^{5} - 1151q^{7} + 7679q^{9} + O(q^{10}) \) \( 11q + 26q^{3} - q^{5} - 1151q^{7} + 7679q^{9} + 5321q^{11} + 648q^{13} + 5990q^{15} - 5631q^{17} + 6859q^{19} - 146310q^{21} + 33824q^{23} + 264190q^{25} + 356012q^{27} - 431054q^{29} + 132436q^{31} + 123730q^{33} - 144753q^{35} + 246150q^{37} - 205200q^{39} - 399770q^{41} + 393373q^{43} + 2069743q^{45} + 102323q^{47} + 1183852q^{49} - 1549438q^{51} + 998648q^{53} + 2281271q^{55} + 370386q^{57} + 933390q^{59} + 2445067q^{61} - 8177599q^{63} - 4404092q^{65} - 1091404q^{67} - 119816q^{69} - 6088678q^{71} - 6928883q^{73} + 12136824q^{75} - 8904315q^{77} + 3181880q^{79} + 17539343q^{81} + 8590644q^{83} - 767505q^{85} - 22198028q^{87} - 11720136q^{89} - 2351012q^{91} + 11190704q^{93} + 3834181q^{95} - 20085436q^{97} + 14272625q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(76))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 19
76.8.a.a \(5\) \(23.741\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(0\) \(-14\) \(-280\) \(414\) \(-\) \(+\) \(q+(-3-\beta _{1})q^{3}+(-56+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
76.8.a.b \(6\) \(23.741\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(0\) \(40\) \(279\) \(-1565\) \(-\) \(-\) \(q+(7-\beta _{1})q^{3}+(47-\beta _{1}-\beta _{2})q^{5}+(-262+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(76))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_0(76)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 2}\)