Properties

Label 1008.2.bh
Level 1008
Weight 2
Character orbit bh
Rep. character \(\chi_{1008}(95,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 96
Newform subspaces 5
Sturm bound 384
Trace bound 3

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Defining parameters

Level: \( N \) = \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1008.bh (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 252 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 5 \)
Sturm bound: \(384\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

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

Total New Old
Modular forms 408 96 312
Cusp forms 360 96 264
Eisenstein series 48 0 48

Trace form

\( 96q + O(q^{10}) \) \( 96q + 24q^{21} - 96q^{25} + 36q^{29} - 12q^{45} + 24q^{57} - 72q^{65} - 24q^{69} + 72q^{77} - 36q^{81} - 36q^{89} + 48q^{93} + O(q^{100}) \)

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.bh.a \(2\) \(8.049\) \(\Q(\sqrt{-3}) \) None \(0\) \(-3\) \(0\) \(1\) \(q+(-1-\zeta_{6})q^{3}+(-1+2\zeta_{6})q^{5}+(2+\cdots)q^{7}+\cdots\)
1008.2.bh.b \(2\) \(8.049\) \(\Q(\sqrt{-3}) \) None \(0\) \(3\) \(0\) \(-1\) \(q+(1+\zeta_{6})q^{3}+(-1+2\zeta_{6})q^{5}+(-2+\cdots)q^{7}+\cdots\)
1008.2.bh.c \(30\) \(8.049\) None \(0\) \(-3\) \(0\) \(-2\)
1008.2.bh.d \(30\) \(8.049\) None \(0\) \(3\) \(0\) \(2\)
1008.2.bh.e \(32\) \(8.049\) None \(0\) \(0\) \(0\) \(0\)

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

\( S_{2}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 3}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ 1
$3$ (\( 1 + 3 T + 3 T^{2} \))(\( 1 - 3 T + 3 T^{2} \))
$5$ (\( 1 - 7 T^{2} + 25 T^{4} \))(\( 1 - 7 T^{2} + 25 T^{4} \))
$7$ (\( 1 - T + 7 T^{2} \))(\( 1 + T + 7 T^{2} \))
$11$ (\( ( 1 + 3 T + 11 T^{2} )^{2} \))(\( ( 1 - 3 T + 11 T^{2} )^{2} \))
$13$ (\( 1 + T - 12 T^{2} + 13 T^{3} + 169 T^{4} \))(\( 1 + T - 12 T^{2} + 13 T^{3} + 169 T^{4} \))
$17$ (\( 1 + 3 T + 20 T^{2} + 51 T^{3} + 289 T^{4} \))(\( 1 + 3 T + 20 T^{2} + 51 T^{3} + 289 T^{4} \))
$19$ (\( 1 - 3 T + 22 T^{2} - 57 T^{3} + 361 T^{4} \))(\( 1 + 3 T + 22 T^{2} + 57 T^{3} + 361 T^{4} \))
$23$ (\( ( 1 + 3 T + 23 T^{2} )^{2} \))(\( ( 1 - 3 T + 23 T^{2} )^{2} \))
$29$ (\( 1 + 15 T + 104 T^{2} + 435 T^{3} + 841 T^{4} \))(\( 1 + 15 T + 104 T^{2} + 435 T^{3} + 841 T^{4} \))
$31$ (\( 1 - 6 T + 43 T^{2} - 186 T^{3} + 961 T^{4} \))(\( 1 + 6 T + 43 T^{2} + 186 T^{3} + 961 T^{4} \))
$37$ (\( 1 + 5 T - 12 T^{2} + 185 T^{3} + 1369 T^{4} \))(\( 1 + 5 T - 12 T^{2} + 185 T^{3} + 1369 T^{4} \))
$41$ (\( 1 + 9 T + 68 T^{2} + 369 T^{3} + 1681 T^{4} \))(\( 1 + 9 T + 68 T^{2} + 369 T^{3} + 1681 T^{4} \))
$43$ (\( ( 1 + 8 T + 43 T^{2} )( 1 + 13 T + 43 T^{2} ) \))(\( ( 1 - 13 T + 43 T^{2} )( 1 - 8 T + 43 T^{2} ) \))
$47$ (\( 1 - 47 T^{2} + 2209 T^{4} \))(\( 1 - 47 T^{2} + 2209 T^{4} \))
$53$ (\( 1 + 9 T + 80 T^{2} + 477 T^{3} + 2809 T^{4} \))(\( 1 + 9 T + 80 T^{2} + 477 T^{3} + 2809 T^{4} \))
$59$ (\( 1 + 12 T + 85 T^{2} + 708 T^{3} + 3481 T^{4} \))(\( 1 - 12 T + 85 T^{2} - 708 T^{3} + 3481 T^{4} \))
$61$ (\( 1 - 10 T + 39 T^{2} - 610 T^{3} + 3721 T^{4} \))(\( 1 - 10 T + 39 T^{2} - 610 T^{3} + 3721 T^{4} \))
$67$ (\( 1 + 18 T + 175 T^{2} + 1206 T^{3} + 4489 T^{4} \))(\( 1 - 18 T + 175 T^{2} - 1206 T^{3} + 4489 T^{4} \))
$71$ (\( ( 1 + 71 T^{2} )^{2} \))(\( ( 1 + 71 T^{2} )^{2} \))
$73$ (\( ( 1 - 10 T + 73 T^{2} )( 1 + 17 T + 73 T^{2} ) \))(\( ( 1 - 10 T + 73 T^{2} )( 1 + 17 T + 73 T^{2} ) \))
$79$ (\( 1 + 18 T + 187 T^{2} + 1422 T^{3} + 6241 T^{4} \))(\( 1 - 18 T + 187 T^{2} - 1422 T^{3} + 6241 T^{4} \))
$83$ (\( 1 + 15 T + 142 T^{2} + 1245 T^{3} + 6889 T^{4} \))(\( 1 - 15 T + 142 T^{2} - 1245 T^{3} + 6889 T^{4} \))
$89$ (\( 1 + 3 T + 92 T^{2} + 267 T^{3} + 7921 T^{4} \))(\( 1 + 3 T + 92 T^{2} + 267 T^{3} + 7921 T^{4} \))
$97$ (\( ( 1 - 19 T + 97 T^{2} )( 1 + 14 T + 97 T^{2} ) \))(\( ( 1 - 19 T + 97 T^{2} )( 1 + 14 T + 97 T^{2} ) \))
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