Properties

Label 76.1.c
Level 76
Weight 1
Character orbit c
Rep. character \(\chi_{76}(37,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 1
Sturm bound 10
Trace bound 0

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Defining parameters

Level: \( N \) = \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 76.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 19 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(10\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(76, [\chi])\).

Total New Old
Modular forms 4 1 3
Cusp forms 1 1 0
Eisenstein series 3 0 3

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 1 0 0 0

Trace form

\(q \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut q^{5} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut -\mathstrut q^{11} \) \(\mathstrut -\mathstrut q^{17} \) \(\mathstrut +\mathstrut q^{19} \) \(\mathstrut +\mathstrut 2q^{23} \) \(\mathstrut +\mathstrut q^{35} \) \(\mathstrut -\mathstrut q^{43} \) \(\mathstrut -\mathstrut q^{45} \) \(\mathstrut -\mathstrut q^{47} \) \(\mathstrut +\mathstrut q^{55} \) \(\mathstrut -\mathstrut q^{61} \) \(\mathstrut -\mathstrut q^{63} \) \(\mathstrut -\mathstrut q^{73} \) \(\mathstrut +\mathstrut q^{77} \) \(\mathstrut +\mathstrut q^{81} \) \(\mathstrut +\mathstrut 2q^{83} \) \(\mathstrut +\mathstrut q^{85} \) \(\mathstrut -\mathstrut q^{95} \) \(\mathstrut -\mathstrut q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(76, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field Image CM RM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
76.1.c.a \(1\) \(0.038\) \(\Q\) \(D_{3}\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-1\) \(-1\) \(q-q^{5}-q^{7}+q^{9}-q^{11}-q^{17}+q^{19}+\cdots\)