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Properties

Label 7.3.b
Level $7$
Weight $3$
Character orbit 7.b
Rep. character $\chi_{7}(6,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $2$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 7.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(2\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(7, [\chi])\).

Total New Old
Modular forms 3 3 0
Cusp forms 1 1 0
Eisenstein series 2 2 0

Trace form

\( q - 3q^{2} + 5q^{4} - 7q^{7} - 3q^{8} + 9q^{9} + O(q^{10}) \) \( q - 3q^{2} + 5q^{4} - 7q^{7} - 3q^{8} + 9q^{9} - 6q^{11} + 21q^{14} - 11q^{16} - 27q^{18} + 18q^{22} + 18q^{23} + 25q^{25} - 35q^{28} - 54q^{29} + 45q^{32} + 45q^{36} - 38q^{37} + 58q^{43} - 30q^{44} - 54q^{46} + 49q^{49} - 75q^{50} - 6q^{53} + 21q^{56} + 162q^{58} - 63q^{63} - 91q^{64} - 118q^{67} + 114q^{71} - 27q^{72} + 114q^{74} + 42q^{77} - 94q^{79} + 81q^{81} - 174q^{86} + 18q^{88} + 90q^{92} - 147q^{98} - 54q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(7, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
7.3.b.a \(1\) \(0.191\) \(\Q\) \(\Q(\sqrt{-7}) \) \(-3\) \(0\) \(0\) \(-7\) \(q-3q^{2}+5q^{4}-7q^{7}-3q^{8}+9q^{9}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + 3 T + 4 T^{2} \)
$3$ \( ( 1 - 3 T )( 1 + 3 T ) \)
$5$ \( ( 1 - 5 T )( 1 + 5 T ) \)
$7$ \( 1 + 7 T \)
$11$ \( 1 + 6 T + 121 T^{2} \)
$13$ \( ( 1 - 13 T )( 1 + 13 T ) \)
$17$ \( ( 1 - 17 T )( 1 + 17 T ) \)
$19$ \( ( 1 - 19 T )( 1 + 19 T ) \)
$23$ \( 1 - 18 T + 529 T^{2} \)
$29$ \( 1 + 54 T + 841 T^{2} \)
$31$ \( ( 1 - 31 T )( 1 + 31 T ) \)
$37$ \( 1 + 38 T + 1369 T^{2} \)
$41$ \( ( 1 - 41 T )( 1 + 41 T ) \)
$43$ \( 1 - 58 T + 1849 T^{2} \)
$47$ \( ( 1 - 47 T )( 1 + 47 T ) \)
$53$ \( 1 + 6 T + 2809 T^{2} \)
$59$ \( ( 1 - 59 T )( 1 + 59 T ) \)
$61$ \( ( 1 - 61 T )( 1 + 61 T ) \)
$67$ \( 1 + 118 T + 4489 T^{2} \)
$71$ \( 1 - 114 T + 5041 T^{2} \)
$73$ \( ( 1 - 73 T )( 1 + 73 T ) \)
$79$ \( 1 + 94 T + 6241 T^{2} \)
$83$ \( ( 1 - 83 T )( 1 + 83 T ) \)
$89$ \( ( 1 - 89 T )( 1 + 89 T ) \)
$97$ \( ( 1 - 97 T )( 1 + 97 T ) \)
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