Properties

Label 25.3.c
Level 25
Weight 3
Character orbit c
Rep. character \(\chi_{25}(7,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 4
Newform subspaces 1
Sturm bound 7
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 25 = 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 25.c (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(7\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(25, [\chi])\).

Total New Old
Modular forms 16 8 8
Cusp forms 4 4 0
Eisenstein series 12 4 8

Trace form

\( 4q - 12q^{6} + O(q^{10}) \) \( 4q - 12q^{6} - 12q^{11} + 44q^{16} + 48q^{21} - 72q^{26} - 152q^{31} + 24q^{36} + 228q^{41} + 168q^{46} - 132q^{51} - 240q^{56} - 112q^{61} + 36q^{66} + 168q^{71} + 20q^{76} - 36q^{81} + 48q^{86} + 288q^{91} + 108q^{96} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(25, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
25.3.c.a \(4\) \(0.681\) \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}+\beta _{3}q^{3}-\beta _{2}q^{4}-3q^{6}-4\beta _{1}q^{7}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 - 7 T^{4} + 256 T^{8} \)
$3$ \( 1 + 63 T^{4} + 6561 T^{8} \)
$5$ 1
$7$ \( 1 - 2302 T^{4} + 5764801 T^{8} \)
$11$ \( ( 1 + 3 T + 121 T^{2} )^{4} \)
$13$ \( 1 - 4222 T^{4} + 815730721 T^{8} \)
$17$ \( 1 - 120817 T^{4} + 6975757441 T^{8} \)
$19$ \( ( 1 - 697 T^{2} + 130321 T^{4} )^{2} \)
$23$ \( 1 - 338782 T^{4} + 78310985281 T^{8} \)
$29$ \( ( 1 - 782 T^{2} + 707281 T^{4} )^{2} \)
$31$ \( ( 1 + 38 T + 961 T^{2} )^{4} \)
$37$ \( 1 + 132578 T^{4} + 3512479453921 T^{8} \)
$41$ \( ( 1 - 57 T + 1681 T^{2} )^{4} \)
$43$ \( 1 + 6484898 T^{4} + 11688200277601 T^{8} \)
$47$ \( 1 + 8816738 T^{4} + 23811286661761 T^{8} \)
$53$ \( 1 - 2892862 T^{4} + 62259690411361 T^{8} \)
$59$ \( ( 1 + 1138 T^{2} + 12117361 T^{4} )^{2} \)
$61$ \( ( 1 + 28 T + 3721 T^{2} )^{4} \)
$67$ \( 1 - 20810017 T^{4} + 406067677556641 T^{8} \)
$71$ \( ( 1 - 42 T + 5041 T^{2} )^{4} \)
$73$ \( 1 + 49190543 T^{4} + 806460091894081 T^{8} \)
$79$ \( ( 1 - 6082 T^{2} + 38950081 T^{4} )^{2} \)
$83$ \( 1 + 27517583 T^{4} + 2252292232139041 T^{8} \)
$89$ \( ( 1 - 15617 T^{2} + 62742241 T^{4} )^{2} \)
$97$ \( 1 - 7798462 T^{4} + 7837433594376961 T^{8} \)
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