Properties

Label 403.2.l
Level 403
Weight 2
Character orbit l
Rep. character \(\chi_{403}(25,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 72
Newform subspaces 3
Sturm bound 74
Trace bound 5

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 403 = 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 403.l (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 403 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 3 \)
Sturm bound: \(74\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

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

Total New Old
Modular forms 80 80 0
Cusp forms 72 72 0
Eisenstein series 8 8 0

Trace form

\( 72q - 4q^{3} - 80q^{4} - 36q^{9} + O(q^{10}) \) \( 72q - 4q^{3} - 80q^{4} - 36q^{9} + 2q^{10} - 12q^{12} + 2q^{13} + 16q^{14} + 64q^{16} - 14q^{22} - 44q^{23} + 26q^{25} + 6q^{26} + 8q^{27} + 24q^{29} - 16q^{30} - 36q^{35} + 36q^{36} + 42q^{38} - 4q^{39} + 14q^{40} - 16q^{42} - 10q^{43} + 22q^{48} + 50q^{49} + 26q^{51} - 32q^{52} + 2q^{53} - 18q^{55} - 44q^{56} + 28q^{61} - 38q^{62} - 4q^{64} - 24q^{65} + 128q^{66} + 10q^{68} - 34q^{69} - 22q^{74} + 24q^{75} - 164q^{77} - 40q^{78} - 70q^{79} - 84q^{81} - 48q^{82} + 40q^{87} - 2q^{88} - 2q^{90} - 88q^{91} + 108q^{92} + 20q^{94} + 40q^{95} + O(q^{100}) \)

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.l.a \(2\) \(3.218\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-3\) \(-3\) \(q+(1-2\zeta_{6})q^{2}+\zeta_{6}q^{3}-q^{4}+(-1+\cdots)q^{5}+\cdots\)
403.2.l.b \(2\) \(3.218\) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(3\) \(3\) \(q+(-1+2\zeta_{6})q^{2}+\zeta_{6}q^{3}-q^{4}+(1+\cdots)q^{5}+\cdots\)
403.2.l.c \(68\) \(3.218\) None \(0\) \(-6\) \(0\) \(0\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 - T^{2} + 4 T^{4} \))(\( 1 - T^{2} + 4 T^{4} \))
$3$ (\( 1 - T - 2 T^{2} - 3 T^{3} + 9 T^{4} \))(\( 1 - T - 2 T^{2} - 3 T^{3} + 9 T^{4} \))
$5$ (\( 1 + 3 T + 8 T^{2} + 15 T^{3} + 25 T^{4} \))(\( 1 - 3 T + 8 T^{2} - 15 T^{3} + 25 T^{4} \))
$7$ (\( ( 1 - T + 7 T^{2} )( 1 + 4 T + 7 T^{2} ) \))(\( ( 1 - 4 T + 7 T^{2} )( 1 + T + 7 T^{2} ) \))
$11$ (\( 1 + 9 T + 38 T^{2} + 99 T^{3} + 121 T^{4} \))(\( 1 - 9 T + 38 T^{2} - 99 T^{3} + 121 T^{4} \))
$13$ (\( 1 - 7 T + 13 T^{2} \))(\( 1 + 2 T + 13 T^{2} \))
$17$ (\( 1 + 3 T - 8 T^{2} + 51 T^{3} + 289 T^{4} \))(\( 1 + 3 T - 8 T^{2} + 51 T^{3} + 289 T^{4} \))
$19$ (\( ( 1 - 8 T + 19 T^{2} )( 1 - T + 19 T^{2} ) \))(\( ( 1 + T + 19 T^{2} )( 1 + 8 T + 19 T^{2} ) \))
$23$ (\( ( 1 + 23 T^{2} )^{2} \))(\( ( 1 + 23 T^{2} )^{2} \))
$29$ (\( ( 1 + 6 T + 29 T^{2} )^{2} \))(\( ( 1 + 6 T + 29 T^{2} )^{2} \))
$31$ (\( 1 - 4 T + 31 T^{2} \))(\( 1 + 4 T + 31 T^{2} \))
$37$ (\( ( 1 - 10 T + 37 T^{2} )( 1 + T + 37 T^{2} ) \))(\( ( 1 - T + 37 T^{2} )( 1 + 10 T + 37 T^{2} ) \))
$41$ (\( 1 - 9 T + 68 T^{2} - 369 T^{3} + 1681 T^{4} \))(\( 1 + 9 T + 68 T^{2} + 369 T^{3} + 1681 T^{4} \))
$43$ (\( 1 - T - 42 T^{2} - 43 T^{3} + 1849 T^{4} \))(\( 1 - T - 42 T^{2} - 43 T^{3} + 1849 T^{4} \))
$47$ (\( 1 - 82 T^{2} + 2209 T^{4} \))(\( 1 - 82 T^{2} + 2209 T^{4} \))
$53$ (\( 1 + 3 T - 44 T^{2} + 159 T^{3} + 2809 T^{4} \))(\( 1 + 3 T - 44 T^{2} + 159 T^{3} + 2809 T^{4} \))
$59$ (\( 1 + 3 T + 62 T^{2} + 177 T^{3} + 3481 T^{4} \))(\( 1 - 3 T + 62 T^{2} - 177 T^{3} + 3481 T^{4} \))
$61$ (\( ( 1 - 10 T + 61 T^{2} )^{2} \))(\( ( 1 - 10 T + 61 T^{2} )^{2} \))
$67$ (\( 1 - 15 T + 142 T^{2} - 1005 T^{3} + 4489 T^{4} \))(\( 1 + 15 T + 142 T^{2} + 1005 T^{3} + 4489 T^{4} \))
$71$ (\( 1 - 15 T + 146 T^{2} - 1065 T^{3} + 5041 T^{4} \))(\( 1 + 15 T + 146 T^{2} + 1065 T^{3} + 5041 T^{4} \))
$73$ (\( 1 + 15 T + 148 T^{2} + 1095 T^{3} + 5329 T^{4} \))(\( 1 - 15 T + 148 T^{2} - 1095 T^{3} + 5329 T^{4} \))
$79$ (\( 1 - 5 T - 54 T^{2} - 395 T^{3} + 6241 T^{4} \))(\( 1 - 5 T - 54 T^{2} - 395 T^{3} + 6241 T^{4} \))
$83$ (\( 1 + 21 T + 230 T^{2} + 1743 T^{3} + 6889 T^{4} \))(\( 1 - 21 T + 230 T^{2} - 1743 T^{3} + 6889 T^{4} \))
$89$ (\( 1 - 130 T^{2} + 7921 T^{4} \))(\( 1 - 130 T^{2} + 7921 T^{4} \))
$97$ (\( 1 - 146 T^{2} + 9409 T^{4} \))(\( 1 - 146 T^{2} + 9409 T^{4} \))
show more
show less