Properties

Label 24.3.e
Level 24
Weight 3
Character orbit e
Rep. character \(\chi_{24}(17,\cdot)\)
Character field \(\Q\)
Dimension 2
Newform subspaces 1
Sturm bound 12
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 24.e (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(24, [\chi])\).

Total New Old
Modular forms 12 2 10
Cusp forms 4 2 2
Eisenstein series 8 0 8

Trace form

\( 2q + 2q^{3} - 12q^{7} - 14q^{9} + O(q^{10}) \) \( 2q + 2q^{3} - 12q^{7} - 14q^{9} + 20q^{13} + 32q^{15} + 4q^{19} - 12q^{21} - 14q^{25} - 46q^{27} - 44q^{31} + 32q^{33} - 12q^{37} + 20q^{39} + 164q^{43} + 64q^{45} - 26q^{49} - 128q^{51} - 64q^{55} + 4q^{57} - 172q^{61} + 84q^{63} + 4q^{67} - 64q^{69} + 164q^{73} - 14q^{75} + 20q^{79} + 34q^{81} + 256q^{85} + 96q^{87} - 120q^{91} - 44q^{93} - 188q^{97} + 64q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(24, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
24.3.e.a \(2\) \(0.654\) \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(0\) \(-12\) \(q+(1+\beta )q^{3}-2\beta q^{5}-6q^{7}+(-7+2\beta )q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(24, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(24, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ \( 1 - 2 T + 9 T^{2} \)
$5$ \( 1 - 18 T^{2} + 625 T^{4} \)
$7$ \( ( 1 + 6 T + 49 T^{2} )^{2} \)
$11$ \( 1 - 210 T^{2} + 14641 T^{4} \)
$13$ \( ( 1 - 10 T + 169 T^{2} )^{2} \)
$17$ \( 1 - 66 T^{2} + 83521 T^{4} \)
$19$ \( ( 1 - 2 T + 361 T^{2} )^{2} \)
$23$ \( 1 - 930 T^{2} + 279841 T^{4} \)
$29$ \( 1 - 1394 T^{2} + 707281 T^{4} \)
$31$ \( ( 1 + 22 T + 961 T^{2} )^{2} \)
$37$ \( ( 1 + 6 T + 1369 T^{2} )^{2} \)
$41$ \( 1 - 2210 T^{2} + 2825761 T^{4} \)
$43$ \( ( 1 - 82 T + 1849 T^{2} )^{2} \)
$47$ \( 1 + 190 T^{2} + 4879681 T^{4} \)
$53$ \( 1 - 1746 T^{2} + 7890481 T^{4} \)
$59$ \( 1 - 1554 T^{2} + 12117361 T^{4} \)
$61$ \( ( 1 + 86 T + 3721 T^{2} )^{2} \)
$67$ \( ( 1 - 2 T + 4489 T^{2} )^{2} \)
$71$ \( 1 + 5406 T^{2} + 25411681 T^{4} \)
$73$ \( ( 1 - 82 T + 5329 T^{2} )^{2} \)
$79$ \( ( 1 - 10 T + 6241 T^{2} )^{2} \)
$83$ \( 1 - 8370 T^{2} + 47458321 T^{4} \)
$89$ \( 1 - 14690 T^{2} + 62742241 T^{4} \)
$97$ \( ( 1 + 94 T + 9409 T^{2} )^{2} \)
show more
show less