Properties

Label 76.2.a
Level $76$
Weight $2$
Character orbit 76.a
Rep. character $\chi_{76}(1,\cdot)$
Character field $\Q$
Dimension $1$
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.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(20\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(76))\).

Total New Old
Modular forms 13 1 12
Cusp forms 8 1 7
Eisenstein series 5 0 5

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.
\(-\)\(+\)\(-\)\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(1\)

Trace form

\( q + 2q^{3} - q^{5} - 3q^{7} + q^{9} + O(q^{10}) \) \( q + 2q^{3} - q^{5} - 3q^{7} + q^{9} + 5q^{11} - 4q^{13} - 2q^{15} - 3q^{17} - q^{19} - 6q^{21} + 8q^{23} - 4q^{25} - 4q^{27} - 2q^{29} + 4q^{31} + 10q^{33} + 3q^{35} + 10q^{37} - 8q^{39} + 10q^{41} + q^{43} - q^{45} - q^{47} + 2q^{49} - 6q^{51} - 4q^{53} - 5q^{55} - 2q^{57} + 6q^{59} - 13q^{61} - 3q^{63} + 4q^{65} - 12q^{67} + 16q^{69} + 2q^{71} + 9q^{73} - 8q^{75} - 15q^{77} + 8q^{79} - 11q^{81} - 12q^{83} + 3q^{85} - 4q^{87} + 12q^{89} + 12q^{91} + 8q^{93} + q^{95} - 8q^{97} + 5q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(76))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 19
76.2.a.a \(1\) \(0.607\) \(\Q\) None \(0\) \(2\) \(-1\) \(-3\) \(-\) \(+\) \(q+2q^{3}-q^{5}-3q^{7}+q^{9}+5q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(76))\) into lower level spaces

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