Properties

Label 7.5.b
Level 7
Weight 5
Character orbit b
Rep. character \(\chi_{7}(6,\cdot)\)
Character field \(\Q\)
Dimension 1
Newform subspaces 1
Sturm bound 3
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 7 \)
Weight: \( k \) \(=\) \( 5 \)
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: \(3\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(7, [\chi])\).

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

Trace form

\( q + q^{2} - 15q^{4} + 49q^{7} - 31q^{8} + 81q^{9} + O(q^{10}) \) \( q + q^{2} - 15q^{4} + 49q^{7} - 31q^{8} + 81q^{9} - 206q^{11} + 49q^{14} + 209q^{16} + 81q^{18} - 206q^{22} - 734q^{23} + 625q^{25} - 735q^{28} + 1234q^{29} + 705q^{32} - 1215q^{36} - 1294q^{37} - 334q^{43} + 3090q^{44} - 734q^{46} + 2401q^{49} + 625q^{50} - 5582q^{53} - 1519q^{56} + 1234q^{58} + 3969q^{63} - 2639q^{64} + 4946q^{67} + 2914q^{71} - 2511q^{72} - 1294q^{74} - 10094q^{77} - 3646q^{79} + 6561q^{81} - 334q^{86} + 6386q^{88} + 11010q^{92} + 2401q^{98} - 16686q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(7, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
7.5.b.a \(1\) \(0.724\) \(\Q\) \(\Q(\sqrt{-7}) \) \(1\) \(0\) \(0\) \(49\) \(q+q^{2}-15q^{4}+7^{2}q^{7}-31q^{8}+3^{4}q^{9}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 - T + 16 T^{2} \)
$3$ \( ( 1 - 9 T )( 1 + 9 T ) \)
$5$ \( ( 1 - 25 T )( 1 + 25 T ) \)
$7$ \( 1 - 49 T \)
$11$ \( 1 + 206 T + 14641 T^{2} \)
$13$ \( ( 1 - 169 T )( 1 + 169 T ) \)
$17$ \( ( 1 - 289 T )( 1 + 289 T ) \)
$19$ \( ( 1 - 361 T )( 1 + 361 T ) \)
$23$ \( 1 + 734 T + 279841 T^{2} \)
$29$ \( 1 - 1234 T + 707281 T^{2} \)
$31$ \( ( 1 - 961 T )( 1 + 961 T ) \)
$37$ \( 1 + 1294 T + 1874161 T^{2} \)
$41$ \( ( 1 - 1681 T )( 1 + 1681 T ) \)
$43$ \( 1 + 334 T + 3418801 T^{2} \)
$47$ \( ( 1 - 2209 T )( 1 + 2209 T ) \)
$53$ \( 1 + 5582 T + 7890481 T^{2} \)
$59$ \( ( 1 - 3481 T )( 1 + 3481 T ) \)
$61$ \( ( 1 - 3721 T )( 1 + 3721 T ) \)
$67$ \( 1 - 4946 T + 20151121 T^{2} \)
$71$ \( 1 - 2914 T + 25411681 T^{2} \)
$73$ \( ( 1 - 5329 T )( 1 + 5329 T ) \)
$79$ \( 1 + 3646 T + 38950081 T^{2} \)
$83$ \( ( 1 - 6889 T )( 1 + 6889 T ) \)
$89$ \( ( 1 - 7921 T )( 1 + 7921 T ) \)
$97$ \( ( 1 - 9409 T )( 1 + 9409 T ) \)
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