Properties

Label 35.2.b
Level 35
Weight 2
Character orbit b
Rep. character \(\chi_{35}(29,\cdot)\)
Character field \(\Q\)
Dimension 2
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 5 \)
Character field: \(\Q\)
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 6 2 4
Cusp forms 2 2 0
Eisenstein series 4 0 4

Trace form

\( 2q - 4q^{4} - 4q^{5} + 4q^{6} + 4q^{9} + O(q^{10}) \) \( 2q - 4q^{4} - 4q^{5} + 4q^{6} + 4q^{9} + 4q^{10} - 6q^{11} + 4q^{14} - 2q^{15} - 8q^{16} + 8q^{20} - 2q^{21} + 6q^{25} + 4q^{26} + 10q^{29} - 8q^{30} + 4q^{31} - 28q^{34} - 2q^{35} - 8q^{36} - 2q^{39} + 4q^{41} + 12q^{44} - 8q^{45} + 24q^{46} - 2q^{49} - 16q^{50} + 14q^{51} + 20q^{54} + 12q^{55} - 20q^{59} + 4q^{60} - 16q^{61} + 16q^{64} - 2q^{65} - 12q^{66} - 12q^{69} - 8q^{70} - 16q^{71} - 8q^{74} + 8q^{75} + 10q^{79} + 16q^{80} + 2q^{81} + 4q^{84} + 14q^{85} - 16q^{86} + 8q^{90} - 2q^{91} + 12q^{94} - 16q^{96} - 12q^{99} + O(q^{100}) \)

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.b.a \(2\) \(0.279\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) \(q+2iq^{2}-iq^{3}-2q^{4}+(-2-i)q^{5}+\cdots\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( ( 1 - 2 T + 2 T^{2} )( 1 + 2 T + 2 T^{2} ) \)
$3$ \( 1 - 5 T^{2} + 9 T^{4} \)
$5$ \( 1 + 4 T + 5 T^{2} \)
$7$ \( 1 + T^{2} \)
$11$ \( ( 1 + 3 T + 11 T^{2} )^{2} \)
$13$ \( 1 - 25 T^{2} + 169 T^{4} \)
$17$ \( 1 + 15 T^{2} + 289 T^{4} \)
$19$ \( ( 1 + 19 T^{2} )^{2} \)
$23$ \( 1 - 10 T^{2} + 529 T^{4} \)
$29$ \( ( 1 - 5 T + 29 T^{2} )^{2} \)
$31$ \( ( 1 - 2 T + 31 T^{2} )^{2} \)
$37$ \( ( 1 - 12 T + 37 T^{2} )( 1 + 12 T + 37 T^{2} ) \)
$41$ \( ( 1 - 2 T + 41 T^{2} )^{2} \)
$43$ \( 1 - 70 T^{2} + 1849 T^{4} \)
$47$ \( 1 - 85 T^{2} + 2209 T^{4} \)
$53$ \( 1 - 70 T^{2} + 2809 T^{4} \)
$59$ \( ( 1 + 10 T + 59 T^{2} )^{2} \)
$61$ \( ( 1 + 8 T + 61 T^{2} )^{2} \)
$67$ \( 1 - 130 T^{2} + 4489 T^{4} \)
$71$ \( ( 1 + 8 T + 71 T^{2} )^{2} \)
$73$ \( ( 1 - 16 T + 73 T^{2} )( 1 + 16 T + 73 T^{2} ) \)
$79$ \( ( 1 - 5 T + 79 T^{2} )^{2} \)
$83$ \( 1 - 150 T^{2} + 6889 T^{4} \)
$89$ \( ( 1 + 89 T^{2} )^{2} \)
$97$ \( 1 - 145 T^{2} + 9409 T^{4} \)
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