Properties

Label 35.2.f
Level 35
Weight 2
Character orbit f
Rep. character \(\chi_{35}(13,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 4
Newform subspaces 1
Sturm bound 8
Trace bound 0

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Defining parameters

Level: \( N \) = \( 35 = 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 35.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 35 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(35, [\chi])\).

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

Trace form

\( 4q - 4q^{2} + 4q^{7} - 8q^{8} + O(q^{10}) \) \( 4q - 4q^{2} + 4q^{7} - 8q^{8} - 4q^{11} + 16q^{16} + 8q^{18} - 20q^{21} + 4q^{22} + 8q^{23} - 20q^{30} + 20q^{35} - 24q^{37} + 20q^{42} - 12q^{43} - 16q^{46} + 20q^{50} + 20q^{51} + 4q^{53} - 16q^{56} + 20q^{57} + 12q^{58} - 8q^{63} - 4q^{67} - 20q^{70} - 24q^{71} - 16q^{72} - 4q^{77} - 20q^{78} + 44q^{81} - 20q^{85} + 24q^{86} + 8q^{88} + 20q^{91} + 20q^{93} - 20q^{95} - 12q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(35, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
35.2.f.a \(4\) \(0.279\) \(\Q(i, \sqrt{10})\) None \(-4\) \(0\) \(0\) \(4\) \(q+(-1-\beta _{2})q^{2}+\beta _{1}q^{3}-\beta _{1}q^{5}+(-\beta _{1}+\cdots)q^{6}+\cdots\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( ( 1 + 2 T + 2 T^{2} + 4 T^{3} + 4 T^{4} )^{2} \)
$3$ \( 1 - 17 T^{4} + 81 T^{8} \)
$5$ \( 1 + 25 T^{4} \)
$7$ \( 1 - 4 T + 8 T^{2} - 28 T^{3} + 49 T^{4} \)
$11$ \( ( 1 + T + 11 T^{2} )^{4} \)
$13$ \( 1 + 103 T^{4} + 28561 T^{8} \)
$17$ \( 1 + 263 T^{4} + 83521 T^{8} \)
$19$ \( ( 1 + 28 T^{2} + 361 T^{4} )^{2} \)
$23$ \( ( 1 - 4 T + 8 T^{2} - 92 T^{3} + 529 T^{4} )^{2} \)
$29$ \( ( 1 - 49 T^{2} + 841 T^{4} )^{2} \)
$31$ \( ( 1 - 52 T^{2} + 961 T^{4} )^{2} \)
$37$ \( ( 1 + 12 T + 72 T^{2} + 444 T^{3} + 1369 T^{4} )^{2} \)
$41$ \( ( 1 + 8 T^{2} + 1681 T^{4} )^{2} \)
$43$ \( ( 1 + 6 T + 18 T^{2} + 258 T^{3} + 1849 T^{4} )^{2} \)
$47$ \( 1 - 2017 T^{4} + 4879681 T^{8} \)
$53$ \( ( 1 - 2 T + 2 T^{2} - 106 T^{3} + 2809 T^{4} )^{2} \)
$59$ \( ( 1 + 28 T^{2} + 3481 T^{4} )^{2} \)
$61$ \( ( 1 - 82 T^{2} + 3721 T^{4} )^{2} \)
$67$ \( ( 1 + 2 T + 2 T^{2} + 134 T^{3} + 4489 T^{4} )^{2} \)
$71$ \( ( 1 + 6 T + 71 T^{2} )^{4} \)
$73$ \( ( 1 + 5329 T^{4} )^{2} \)
$79$ \( ( 1 + 11 T^{2} + 6241 T^{4} )^{2} \)
$83$ \( 1 + 7538 T^{4} + 47458321 T^{8} \)
$89$ \( ( 1 + 138 T^{2} + 7921 T^{4} )^{2} \)
$97$ \( 1 + 16903 T^{4} + 88529281 T^{8} \)
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