Properties

Label 76.6.a
Level $76$
Weight $6$
Character orbit 76.a
Rep. character $\chi_{76}(1,\cdot)$
Character field $\Q$
Dimension $7$
Newform subspaces $2$
Sturm bound $60$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 76.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(60\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(76))\).

Total New Old
Modular forms 53 7 46
Cusp forms 47 7 40
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.
\(-\)\(+\)\(-\)\(4\)
\(-\)\(-\)\(+\)\(3\)
Plus space\(+\)\(3\)
Minus space\(-\)\(4\)

Trace form

\( 7q + 2q^{3} - 119q^{5} + 17q^{7} + 1067q^{9} + O(q^{10}) \) \( 7q + 2q^{3} - 119q^{5} + 17q^{7} + 1067q^{9} - 523q^{11} + 732q^{13} + 1094q^{15} - 2909q^{17} - 361q^{19} + 942q^{21} + 2672q^{23} + 7352q^{25} - 7156q^{27} + 7754q^{29} - 11644q^{31} + 24286q^{33} + 23403q^{35} - 21258q^{37} + 5736q^{39} - 24450q^{41} - 12631q^{43} - 37151q^{45} - 1933q^{47} + 20390q^{49} + 81146q^{51} - 46884q^{53} - 100265q^{55} - 6498q^{57} + 21286q^{59} + 27413q^{61} - 7471q^{63} + 44516q^{65} + 1972q^{67} - 70616q^{69} + 87738q^{71} - 60673q^{73} - 125928q^{75} - 13529q^{77} + 142072q^{79} + 81155q^{81} - 127324q^{83} + 29301q^{85} + 125020q^{87} - 110132q^{89} + 60332q^{91} + 147392q^{93} + 36461q^{95} + 194176q^{97} + 146981q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(76))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 19
76.6.a.a \(3\) \(12.189\) 3.3.272193.1 None \(0\) \(-8\) \(-9\) \(-13\) \(-\) \(-\) \(q+(-3-\beta _{1}-\beta _{2})q^{3}+(-2+3\beta _{1}+\cdots)q^{5}+\cdots\)
76.6.a.b \(4\) \(12.189\) \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(0\) \(10\) \(-110\) \(30\) \(-\) \(+\) \(q+(3+\beta _{3})q^{3}+(-26+\beta _{1}+2\beta _{2}+3\beta _{3})q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(76))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(76)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(38))\)\(^{\oplus 2}\)