Properties

Label 76.1.c
Level 76
Weight 1
Character orbit c
Rep. character \(\chi_{76}(37,\cdot)\)
Character field \(\Q\)
Dimension 1
Newform subspaces 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: \(\Q\)
Newform subspaces: \( 1 \)
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

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

Decomposition of \(S_{1}^{\mathrm{new}}(76, [\chi])\) into newform subspaces

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 \(0\) \(0\) \(-1\) \(-1\) \(q-q^{5}-q^{7}+q^{9}-q^{11}-q^{17}+q^{19}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ \( ( 1 - T )( 1 + T ) \)
$5$ \( 1 + T + T^{2} \)
$7$ \( 1 + T + T^{2} \)
$11$ \( 1 + T + T^{2} \)
$13$ \( ( 1 - T )( 1 + T ) \)
$17$ \( 1 + T + T^{2} \)
$19$ \( 1 - T \)
$23$ \( ( 1 - T )^{2} \)
$29$ \( ( 1 - T )( 1 + T ) \)
$31$ \( ( 1 - T )( 1 + T ) \)
$37$ \( ( 1 - T )( 1 + T ) \)
$41$ \( ( 1 - T )( 1 + T ) \)
$43$ \( 1 + T + T^{2} \)
$47$ \( 1 + T + T^{2} \)
$53$ \( ( 1 - T )( 1 + T ) \)
$59$ \( ( 1 - T )( 1 + T ) \)
$61$ \( 1 + T + T^{2} \)
$67$ \( ( 1 - T )( 1 + T ) \)
$71$ \( ( 1 - T )( 1 + T ) \)
$73$ \( 1 + T + T^{2} \)
$79$ \( ( 1 - T )( 1 + T ) \)
$83$ \( ( 1 - T )^{2} \)
$89$ \( ( 1 - T )( 1 + T ) \)
$97$ \( ( 1 - T )( 1 + T ) \)
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