Properties

Label 4020.2.g
Level 4020
Weight 2
Character orbit g
Rep. character \(\chi_{4020}(1609,\cdot)\)
Character field \(\Q\)
Dimension 64
Newform subspaces 3
Sturm bound 1632
Trace bound 1

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Defining parameters

Level: \( N \) \(=\) \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4020.g (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(1632\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4020, [\chi])\).

Total New Old
Modular forms 828 64 764
Cusp forms 804 64 740
Eisenstein series 24 0 24

Trace form

\( 64q - 4q^{5} - 64q^{9} + O(q^{10}) \) \( 64q - 4q^{5} - 64q^{9} + 16q^{11} + 4q^{15} - 8q^{21} + 8q^{25} - 32q^{29} - 8q^{31} - 4q^{35} + 24q^{41} + 4q^{45} - 56q^{49} + 8q^{55} - 32q^{59} + 24q^{61} + 4q^{65} + 8q^{75} - 24q^{79} + 64q^{81} - 8q^{85} - 24q^{89} + 24q^{91} + 32q^{95} - 16q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(4020, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
4020.2.g.a \(2\) \(32.100\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+iq^{3}+(1-2i)q^{5}-q^{9}+2iq^{13}+\cdots\)
4020.2.g.b \(24\) \(32.100\) None \(0\) \(0\) \(-4\) \(0\)
4020.2.g.c \(38\) \(32.100\) None \(0\) \(0\) \(-2\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(4020, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4020, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(335, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(670, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1005, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1340, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2010, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ (\( 1 + T^{2} \))
$5$ (\( 1 - 2 T + 5 T^{2} \))
$7$ (\( ( 1 - 7 T^{2} )^{2} \))
$11$ (\( ( 1 + 11 T^{2} )^{2} \))
$13$ (\( 1 - 22 T^{2} + 169 T^{4} \))
$17$ (\( ( 1 - 8 T + 17 T^{2} )( 1 + 8 T + 17 T^{2} ) \))
$19$ (\( ( 1 + 19 T^{2} )^{2} \))
$23$ (\( 1 + 18 T^{2} + 529 T^{4} \))
$29$ (\( ( 1 + 6 T + 29 T^{2} )^{2} \))
$31$ (\( ( 1 + 2 T + 31 T^{2} )^{2} \))
$37$ (\( ( 1 - 37 T^{2} )^{2} \))
$41$ (\( ( 1 + 6 T + 41 T^{2} )^{2} \))
$43$ (\( 1 - 70 T^{2} + 1849 T^{4} \))
$47$ (\( ( 1 - 47 T^{2} )^{2} \))
$53$ (\( ( 1 - 14 T + 53 T^{2} )( 1 + 14 T + 53 T^{2} ) \))
$59$ (\( ( 1 + 2 T + 59 T^{2} )^{2} \))
$61$ (\( ( 1 + 10 T + 61 T^{2} )^{2} \))
$67$ (\( 1 + T^{2} \))
$71$ (\( ( 1 + 10 T + 71 T^{2} )^{2} \))
$73$ (\( 1 - 82 T^{2} + 5329 T^{4} \))
$79$ (\( ( 1 - 14 T + 79 T^{2} )^{2} \))
$83$ (\( 1 - 22 T^{2} + 6889 T^{4} \))
$89$ (\( ( 1 - 2 T + 89 T^{2} )^{2} \))
$97$ (\( 1 + 2 T^{2} + 9409 T^{4} \))
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