Properties

Label 432.2.c
Level 432
Weight 2
Character orbit c
Rep. character \(\chi_{432}(431,\cdot)\)
Character field \(\Q\)
Dimension 8
Newform subspaces 3
Sturm bound 144
Trace bound 13

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 432.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(144\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(432, [\chi])\).

Total New Old
Modular forms 90 8 82
Cusp forms 54 8 46
Eisenstein series 36 0 36

Trace form

\( 8q + O(q^{10}) \) \( 8q - 4q^{13} + 4q^{25} + 52q^{37} - 16q^{49} - 44q^{61} - 16q^{73} - 72q^{85} + 8q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(432, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
432.2.c.a \(2\) \(3.450\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{6}q^{7}-5q^{13}-\zeta_{6}q^{19}+5q^{25}+\cdots\)
432.2.c.b \(2\) \(3.450\) \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{6}q^{7}+7q^{13}-5\zeta_{6}q^{19}+5q^{25}+\cdots\)
432.2.c.c \(4\) \(3.450\) \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{5}+\zeta_{12}^{2}q^{7}-\zeta_{12}^{3}q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(432, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(432, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(108, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( \))(\( \))(\( \))
$3$ (\( \))(\( \))(\( \))
$5$ (\( ( 1 - 5 T^{2} )^{2} \))(\( ( 1 - 5 T^{2} )^{2} \))(\( ( 1 - T^{2} + 25 T^{4} )^{2} \))
$7$ (\( ( 1 - T + 7 T^{2} )( 1 + T + 7 T^{2} ) \))(\( ( 1 - 5 T + 7 T^{2} )( 1 + 5 T + 7 T^{2} ) \))(\( ( 1 - 5 T + 7 T^{2} )^{2}( 1 + 5 T + 7 T^{2} )^{2} \))
$11$ (\( ( 1 + 11 T^{2} )^{2} \))(\( ( 1 + 11 T^{2} )^{2} \))(\( ( 1 - 5 T^{2} + 121 T^{4} )^{2} \))
$13$ (\( ( 1 + 5 T + 13 T^{2} )^{2} \))(\( ( 1 - 7 T + 13 T^{2} )^{2} \))(\( ( 1 + 2 T + 13 T^{2} )^{4} \))
$17$ (\( ( 1 - 17 T^{2} )^{2} \))(\( ( 1 - 17 T^{2} )^{2} \))(\( ( 1 + 2 T^{2} + 289 T^{4} )^{2} \))
$19$ (\( ( 1 - 7 T + 19 T^{2} )( 1 + 7 T + 19 T^{2} ) \))(\( ( 1 - T + 19 T^{2} )( 1 + T + 19 T^{2} ) \))(\( ( 1 + 10 T^{2} + 361 T^{4} )^{2} \))
$23$ (\( ( 1 + 23 T^{2} )^{2} \))(\( ( 1 + 23 T^{2} )^{2} \))(\( ( 1 + 23 T^{2} )^{4} \))
$29$ (\( ( 1 - 29 T^{2} )^{2} \))(\( ( 1 - 29 T^{2} )^{2} \))(\( ( 1 - 22 T^{2} + 841 T^{4} )^{2} \))
$31$ (\( ( 1 - 4 T + 31 T^{2} )( 1 + 4 T + 31 T^{2} ) \))(\( ( 1 - 4 T + 31 T^{2} )( 1 + 4 T + 31 T^{2} ) \))(\( ( 1 - 35 T^{2} + 961 T^{4} )^{2} \))
$37$ (\( ( 1 - 11 T + 37 T^{2} )^{2} \))(\( ( 1 + T + 37 T^{2} )^{2} \))(\( ( 1 - 8 T + 37 T^{2} )^{4} \))
$41$ (\( ( 1 - 41 T^{2} )^{2} \))(\( ( 1 - 41 T^{2} )^{2} \))(\( ( 1 - 41 T^{2} )^{4} \))
$43$ (\( ( 1 - 8 T + 43 T^{2} )( 1 + 8 T + 43 T^{2} ) \))(\( ( 1 - 8 T + 43 T^{2} )( 1 + 8 T + 43 T^{2} ) \))(\( ( 1 - 8 T + 43 T^{2} )^{2}( 1 + 8 T + 43 T^{2} )^{2} \))
$47$ (\( ( 1 + 47 T^{2} )^{2} \))(\( ( 1 + 47 T^{2} )^{2} \))(\( ( 1 - 14 T^{2} + 2209 T^{4} )^{2} \))
$53$ (\( ( 1 - 53 T^{2} )^{2} \))(\( ( 1 - 53 T^{2} )^{2} \))(\( ( 1 - 25 T^{2} + 2809 T^{4} )^{2} \))
$59$ (\( ( 1 + 59 T^{2} )^{2} \))(\( ( 1 + 59 T^{2} )^{2} \))(\( ( 1 + 10 T^{2} + 3481 T^{4} )^{2} \))
$61$ (\( ( 1 + T + 61 T^{2} )^{2} \))(\( ( 1 + 13 T + 61 T^{2} )^{2} \))(\( ( 1 + 4 T + 61 T^{2} )^{4} \))
$67$ (\( ( 1 - 5 T + 67 T^{2} )( 1 + 5 T + 67 T^{2} ) \))(\( ( 1 - 11 T + 67 T^{2} )( 1 + 11 T + 67 T^{2} ) \))(\( ( 1 - 16 T + 67 T^{2} )^{2}( 1 + 16 T + 67 T^{2} )^{2} \))
$71$ (\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 34 T^{2} + 5041 T^{4} )^{2} \))
$73$ (\( ( 1 - 7 T + 73 T^{2} )^{2} \))(\( ( 1 + 17 T + 73 T^{2} )^{2} \))(\( ( 1 - T + 73 T^{2} )^{4} \))
$79$ (\( ( 1 - 17 T + 79 T^{2} )( 1 + 17 T + 79 T^{2} ) \))(\( ( 1 - 13 T + 79 T^{2} )( 1 + 13 T + 79 T^{2} ) \))(\( ( 1 - 146 T^{2} + 6241 T^{4} )^{2} \))
$83$ (\( ( 1 + 83 T^{2} )^{2} \))(\( ( 1 + 83 T^{2} )^{2} \))(\( ( 1 + 139 T^{2} + 6889 T^{4} )^{2} \))
$89$ (\( ( 1 - 89 T^{2} )^{2} \))(\( ( 1 - 89 T^{2} )^{2} \))(\( ( 1 - 142 T^{2} + 7921 T^{4} )^{2} \))
$97$ (\( ( 1 - 19 T + 97 T^{2} )^{2} \))(\( ( 1 + 5 T + 97 T^{2} )^{2} \))(\( ( 1 + 5 T + 97 T^{2} )^{4} \))
show more
show less