Properties

Label 432.2.k
Level 432
Weight 2
Character orbit k
Rep. character \(\chi_{432}(109,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 64
Newform subspaces 4
Sturm bound 144
Trace bound 13

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Defining parameters

Level: \( N \) = \( 432 = 2^{4} \cdot 3^{3} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 432.k (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 16 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 4 \)
Sturm bound: \(144\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

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

Total New Old
Modular forms 156 64 92
Cusp forms 132 64 68
Eisenstein series 24 0 24

Trace form

\( 64q + O(q^{10}) \) \( 64q - 4q^{10} + 36q^{16} + 8q^{19} + 4q^{22} + 12q^{28} + 20q^{34} + 4q^{40} + 16q^{43} - 48q^{46} - 64q^{49} - 20q^{52} - 48q^{58} - 16q^{61} - 24q^{64} + 64q^{67} - 120q^{70} - 48q^{76} - 16q^{79} + 16q^{85} - 116q^{88} - 24q^{91} - 12q^{94} + O(q^{100}) \)

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.k.a \(4\) \(3.450\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}+\zeta_{8}^{3})q^{2}-2q^{4}-\zeta_{8}q^{5}+3\zeta_{8}^{2}q^{7}+\cdots\)
432.2.k.b \(4\) \(3.450\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{8}+\zeta_{8}^{3})q^{2}-2q^{4}-\zeta_{8}q^{5}-3\zeta_{8}^{2}q^{7}+\cdots\)
432.2.k.c \(24\) \(3.450\) None \(0\) \(0\) \(0\) \(0\)
432.2.k.d \(32\) \(3.450\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(432, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( ( 1 + 2 T^{2} )^{2} \))(\( ( 1 + 2 T^{2} )^{2} \))
$3$ 1
$5$ (\( 1 + 31 T^{4} + 625 T^{8} \))(\( 1 + 31 T^{4} + 625 T^{8} \))
$7$ (\( ( 1 - 5 T^{2} + 49 T^{4} )^{2} \))(\( ( 1 - 5 T^{2} + 49 T^{4} )^{2} \))
$11$ (\( 1 + 199 T^{4} + 14641 T^{8} \))(\( 1 - 233 T^{4} + 14641 T^{8} \))
$13$ (\( ( 1 + 4 T + 13 T^{2} )^{2}( 1 + 6 T + 13 T^{2} )^{2} \))(\( ( 1 - 6 T + 13 T^{2} )^{2}( 1 + 4 T + 13 T^{2} )^{2} \))
$17$ (\( ( 1 + 16 T^{2} + 289 T^{4} )^{2} \))(\( ( 1 + 16 T^{2} + 289 T^{4} )^{2} \))
$19$ (\( ( 1 + 4 T + 8 T^{2} + 76 T^{3} + 361 T^{4} )^{2} \))(\( ( 1 - 8 T + 32 T^{2} - 152 T^{3} + 361 T^{4} )^{2} \))
$23$ (\( ( 1 - 14 T^{2} + 529 T^{4} )^{2} \))(\( ( 1 - 38 T^{2} + 529 T^{4} )^{2} \))
$29$ (\( 1 - 1646 T^{4} + 707281 T^{8} \))(\( ( 1 - 40 T^{2} + 841 T^{4} )( 1 + 40 T^{2} + 841 T^{4} ) \))
$31$ (\( ( 1 + T + 31 T^{2} )^{4} \))(\( ( 1 + 7 T + 31 T^{2} )^{4} \))
$37$ (\( ( 1 - 8 T + 32 T^{2} - 296 T^{3} + 1369 T^{4} )^{2} \))(\( ( 1 + 4 T + 8 T^{2} + 148 T^{3} + 1369 T^{4} )^{2} \))
$41$ (\( ( 1 - 74 T^{2} + 1681 T^{4} )^{2} \))(\( ( 1 - 50 T^{2} + 1681 T^{4} )^{2} \))
$43$ (\( ( 1 - 2 T + 2 T^{2} - 86 T^{3} + 1849 T^{4} )^{2} \))(\( ( 1 - 14 T + 98 T^{2} - 602 T^{3} + 1849 T^{4} )^{2} \))
$47$ (\( ( 1 + 76 T^{2} + 2209 T^{4} )^{2} \))(\( ( 1 + 76 T^{2} + 2209 T^{4} )^{2} \))
$53$ (\( 1 - 5393 T^{4} + 7890481 T^{8} \))(\( 1 + 5407 T^{4} + 7890481 T^{8} \))
$59$ (\( 1 - 6638 T^{4} + 12117361 T^{8} \))(\( 1 - 6638 T^{4} + 12117361 T^{8} \))
$61$ (\( ( 1 + 4 T + 8 T^{2} + 244 T^{3} + 3721 T^{4} )^{2} \))(\( ( 1 - 20 T + 200 T^{2} - 1220 T^{3} + 3721 T^{4} )^{2} \))
$67$ (\( ( 1 + 10 T + 50 T^{2} + 670 T^{3} + 4489 T^{4} )^{2} \))(\( ( 1 - 2 T + 2 T^{2} - 134 T^{3} + 4489 T^{4} )^{2} \))
$71$ (\( ( 1 - 140 T^{2} + 5041 T^{4} )^{2} \))(\( ( 1 + 100 T^{2} + 5041 T^{4} )^{2} \))
$73$ (\( ( 1 - 137 T^{2} + 5329 T^{4} )^{2} \))(\( ( 1 + 79 T^{2} + 5329 T^{4} )^{2} \))
$79$ (\( ( 1 - 14 T + 79 T^{2} )^{4} \))(\( ( 1 - 2 T + 79 T^{2} )^{4} \))
$83$ (\( 1 - 89 T^{4} + 47458321 T^{8} \))(\( 1 - 11753 T^{4} + 47458321 T^{8} \))
$89$ (\( ( 1 + 64 T^{2} + 7921 T^{4} )^{2} \))(\( ( 1 - 176 T^{2} + 7921 T^{4} )^{2} \))
$97$ (\( ( 1 - 5 T + 97 T^{2} )^{4} \))(\( ( 1 + 7 T + 97 T^{2} )^{4} \))
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