Properties

Label 403.2.c
Level 403
Weight 2
Character orbit c
Rep. character \(\chi_{403}(311,\cdot)\)
Character field \(\Q\)
Dimension 34
Newform subspaces 2
Sturm bound 74
Trace bound 1

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Defining parameters

Level: \( N \) = \( 403 = 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 403.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(74\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(403, [\chi])\).

Total New Old
Modular forms 38 34 4
Cusp forms 34 34 0
Eisenstein series 4 0 4

Trace form

\( 34q - 32q^{4} + 22q^{9} + O(q^{10}) \) \( 34q - 32q^{4} + 22q^{9} + 4q^{10} - 8q^{12} + 6q^{13} - 16q^{14} + 36q^{16} - 12q^{17} - 16q^{22} - 16q^{23} - 18q^{25} + 18q^{26} + 12q^{27} + 40q^{30} + 12q^{35} - 40q^{36} + 12q^{38} - 4q^{39} + 28q^{40} + 28q^{42} - 24q^{43} + 16q^{48} - 58q^{49} - 8q^{51} - 72q^{52} - 20q^{53} + 36q^{55} + 8q^{56} + 36q^{61} + 8q^{62} - 60q^{64} - 42q^{65} - 68q^{66} + 56q^{68} + 4q^{69} + 16q^{74} - 44q^{75} - 28q^{77} - 20q^{78} + 32q^{79} - 38q^{81} + 12q^{82} - 40q^{87} + 80q^{88} + 68q^{90} + 10q^{91} + 12q^{92} + 88q^{94} + 20q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(403, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
403.2.c.a \(2\) \(3.218\) \(\Q(\sqrt{-1}) \) None \(0\) \(4\) \(0\) \(0\) \(q+2q^{3}+2q^{4}+4iq^{5}-2iq^{7}+q^{9}+\cdots\)
403.2.c.b \(32\) \(3.218\) None \(0\) \(-4\) \(0\) \(0\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( ( 1 - 2 T^{2} )^{2} \))
$3$ (\( ( 1 - 2 T + 3 T^{2} )^{2} \))
$5$ (\( ( 1 - 2 T + 5 T^{2} )( 1 + 2 T + 5 T^{2} ) \))
$7$ (\( 1 - 10 T^{2} + 49 T^{4} \))
$11$ (\( 1 - 21 T^{2} + 121 T^{4} \))
$13$ (\( 1 + 4 T + 13 T^{2} \))
$17$ (\( ( 1 + 2 T + 17 T^{2} )^{2} \))
$19$ (\( 1 - 34 T^{2} + 361 T^{4} \))
$23$ (\( ( 1 + 4 T + 23 T^{2} )^{2} \))
$29$ (\( ( 1 - 8 T + 29 T^{2} )^{2} \))
$31$ (\( 1 + T^{2} \))
$37$ (\( 1 - 65 T^{2} + 1369 T^{4} \))
$41$ (\( 1 - 66 T^{2} + 1681 T^{4} \))
$43$ (\( ( 1 - 4 T + 43 T^{2} )^{2} \))
$47$ (\( 1 - 90 T^{2} + 2209 T^{4} \))
$53$ (\( ( 1 + 4 T + 53 T^{2} )^{2} \))
$59$ (\( 1 - 82 T^{2} + 3481 T^{4} \))
$61$ (\( ( 1 - 10 T + 61 T^{2} )^{2} \))
$67$ (\( 1 + 122 T^{2} + 4489 T^{4} \))
$71$ (\( 1 - 106 T^{2} + 5041 T^{4} \))
$73$ (\( 1 - 97 T^{2} + 5329 T^{4} \))
$79$ (\( ( 1 + 16 T + 79 T^{2} )^{2} \))
$83$ (\( 1 - 22 T^{2} + 6889 T^{4} \))
$89$ (\( 1 + 47 T^{2} + 7921 T^{4} \))
$97$ (\( 1 - 190 T^{2} + 9409 T^{4} \))
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