Properties

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

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 76.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(76))\) into irreducible Hecke orbits

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

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