Properties

Label 1008.2.h
Level 1008
Weight 2
Character orbit h
Rep. character \(\chi_{1008}(575,\cdot)\)
Character field \(\Q\)
Dimension 12
Newform subspaces 2
Sturm bound 384
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1008.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(384\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1008, [\chi])\).

Total New Old
Modular forms 216 12 204
Cusp forms 168 12 156
Eisenstein series 48 0 48

Trace form

\( 12q + O(q^{10}) \) \( 12q - 12q^{25} - 24q^{37} - 12q^{49} + 24q^{61} - 24q^{85} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1008, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
1008.2.h.a \(4\) \(8.049\) \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{2}q^{5}+\zeta_{8}q^{7}+4\zeta_{8}^{3}q^{11}-4q^{13}+\cdots\)
1008.2.h.b \(8\) \(8.049\) \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{24}^{2}+\zeta_{24}^{7})q^{5}-\zeta_{24}q^{7}+(-\zeta_{24}^{3}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1008, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ 1
$3$ 1
$5$ (\( ( 1 - 8 T^{2} + 25 T^{4} )^{2} \))(\( ( 1 - 4 T^{2} + 6 T^{4} - 100 T^{6} + 625 T^{8} )^{2} \))
$7$ (\( ( 1 + T^{2} )^{2} \))(\( ( 1 + T^{2} )^{4} \))
$11$ (\( ( 1 - 10 T^{2} + 121 T^{4} )^{2} \))(\( ( 1 + 16 T^{2} + 114 T^{4} + 1936 T^{6} + 14641 T^{8} )^{2} \))
$13$ (\( ( 1 + 4 T + 13 T^{2} )^{4} \))(\( ( 1 - 2 T + 13 T^{2} )^{8} \))
$17$ (\( ( 1 - 32 T^{2} + 289 T^{4} )^{2} \))(\( ( 1 - 52 T^{2} + 1206 T^{4} - 15028 T^{6} + 83521 T^{8} )^{2} \))
$19$ (\( ( 1 + 26 T^{2} + 361 T^{4} )^{2} \))(\( ( 1 - 44 T^{2} + 1014 T^{4} - 15884 T^{6} + 130321 T^{8} )^{2} \))
$23$ (\( ( 1 + 14 T^{2} + 529 T^{4} )^{2} \))(\( ( 1 + 64 T^{2} + 1890 T^{4} + 33856 T^{6} + 279841 T^{8} )^{2} \))
$29$ (\( ( 1 - 8 T^{2} + 841 T^{4} )^{2} \))(\( ( 1 - 64 T^{2} + 2514 T^{4} - 53824 T^{6} + 707281 T^{8} )^{2} \))
$31$ (\( ( 1 - 31 T^{2} )^{4} \))(\( ( 1 - 28 T^{2} + 390 T^{4} - 26908 T^{6} + 923521 T^{8} )^{2} \))
$37$ (\( ( 1 - 2 T + 37 T^{2} )^{4} \))(\( ( 1 + 8 T + 42 T^{2} + 296 T^{3} + 1369 T^{4} )^{4} \))
$41$ (\( ( 1 - 32 T^{2} + 1681 T^{4} )^{2} \))(\( ( 1 - 52 T^{2} + 3606 T^{4} - 87412 T^{6} + 2825761 T^{8} )^{2} \))
$43$ (\( ( 1 - 22 T^{2} + 1849 T^{4} )^{2} \))(\( ( 1 - 70 T^{2} + 1849 T^{4} )^{4} \))
$47$ (\( ( 1 + 47 T^{2} )^{4} \))(\( ( 1 + 22 T^{2} + 2209 T^{4} )^{4} \))
$53$ (\( ( 1 - 8 T^{2} + 2809 T^{4} )^{2} \))(\( ( 1 - 56 T^{2} + 2809 T^{4} )^{4} \))
$59$ (\( ( 1 - 10 T^{2} + 3481 T^{4} )^{2} \))(\( ( 1 + 110 T^{2} + 3481 T^{4} )^{4} \))
$61$ (\( ( 1 - 6 T + 61 T^{2} )^{4} \))(\( ( 1 + 110 T^{2} + 3721 T^{4} )^{4} \))
$67$ (\( ( 1 - 67 T^{2} )^{4} \))(\( ( 1 + 44 T^{2} + 2550 T^{4} + 197516 T^{6} + 20151121 T^{8} )^{2} \))
$71$ (\( ( 1 + 110 T^{2} + 5041 T^{4} )^{2} \))(\( ( 1 + 160 T^{2} + 14754 T^{4} + 806560 T^{6} + 25411681 T^{8} )^{2} \))
$73$ (\( ( 1 + 8 T + 73 T^{2} )^{4} \))(\( ( 1 - 8 T + 150 T^{2} - 584 T^{3} + 5329 T^{4} )^{4} \))
$79$ (\( ( 1 - 79 T^{2} )^{4} \))(\( ( 1 - 50 T^{2} + 6241 T^{4} )^{4} \))
$83$ (\( ( 1 + 38 T^{2} + 6889 T^{4} )^{2} \))(\( ( 1 - 116 T^{2} + 10230 T^{4} - 799124 T^{6} + 47458321 T^{8} )^{2} \))
$89$ (\( ( 1 - 80 T^{2} + 7921 T^{4} )^{2} \))(\( ( 1 - 340 T^{2} + 44694 T^{4} - 2693140 T^{6} + 62742241 T^{8} )^{2} \))
$97$ (\( ( 1 + 16 T + 97 T^{2} )^{4} \))(\( ( 1 - 16 T + 246 T^{2} - 1552 T^{3} + 9409 T^{4} )^{4} \))
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