Properties

Label 3024.2.cx
Level 3024
Weight 2
Character orbit cx
Rep. character \(\chi_{3024}(559,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 96
Newform subspaces 11
Sturm bound 1152
Trace bound 11

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Defining parameters

Level: \( N \) = \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3024.cx (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 252 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 11 \)
Sturm bound: \(1152\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3024, [\chi])\).

Total New Old
Modular forms 1224 96 1128
Cusp forms 1080 96 984
Eisenstein series 144 0 144

Trace form

\( 96q + O(q^{10}) \) \( 96q + 48q^{25} - 24q^{29} - 24q^{65} + 24q^{77} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3024, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3024.2.cx.a \(2\) \(24.147\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-3\) \(-5\) \(q+(-1-\zeta_{6})q^{5}+(-2-\zeta_{6})q^{7}+(4+\cdots)q^{11}+\cdots\)
3024.2.cx.b \(2\) \(24.147\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-3\) \(-4\) \(q+(-1-\zeta_{6})q^{5}+(-1-2\zeta_{6})q^{7}+(2+\cdots)q^{11}+\cdots\)
3024.2.cx.c \(2\) \(24.147\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-3\) \(4\) \(q+(-1-\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}+(-2+\cdots)q^{11}+\cdots\)
3024.2.cx.d \(2\) \(24.147\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-3\) \(5\) \(q+(-1-\zeta_{6})q^{5}+(2+\zeta_{6})q^{7}+(-4+\cdots)q^{11}+\cdots\)
3024.2.cx.e \(2\) \(24.147\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(-1\) \(q+(1+\zeta_{6})q^{5}+(1-3\zeta_{6})q^{7}+(-2+\zeta_{6})q^{11}+\cdots\)
3024.2.cx.f \(2\) \(24.147\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(-1\) \(q+(1+\zeta_{6})q^{5}+(-2+3\zeta_{6})q^{7}+(4-2\zeta_{6})q^{11}+\cdots\)
3024.2.cx.g \(2\) \(24.147\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(1\) \(q+(1+\zeta_{6})q^{5}+(2-3\zeta_{6})q^{7}+(-4+2\zeta_{6})q^{11}+\cdots\)
3024.2.cx.h \(2\) \(24.147\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(1\) \(q+(1+\zeta_{6})q^{5}+(-1+3\zeta_{6})q^{7}+(2-\zeta_{6})q^{11}+\cdots\)
3024.2.cx.i \(24\) \(24.147\) None \(0\) \(0\) \(0\) \(-6\)
3024.2.cx.j \(24\) \(24.147\) None \(0\) \(0\) \(0\) \(6\)
3024.2.cx.k \(32\) \(24.147\) None \(0\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(3024, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3024, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ 1
$3$ 1
$5$ (\( 1 + 3 T + 8 T^{2} + 15 T^{3} + 25 T^{4} \))(\( 1 + 3 T + 8 T^{2} + 15 T^{3} + 25 T^{4} \))(\( 1 + 3 T + 8 T^{2} + 15 T^{3} + 25 T^{4} \))(\( 1 + 3 T + 8 T^{2} + 15 T^{3} + 25 T^{4} \))(\( 1 - 3 T + 8 T^{2} - 15 T^{3} + 25 T^{4} \))(\( 1 - 3 T + 8 T^{2} - 15 T^{3} + 25 T^{4} \))(\( 1 - 3 T + 8 T^{2} - 15 T^{3} + 25 T^{4} \))(\( 1 - 3 T + 8 T^{2} - 15 T^{3} + 25 T^{4} \))
$7$ (\( 1 + 5 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 - 4 T + 7 T^{2} \))(\( 1 - 5 T + 7 T^{2} \))(\( 1 + T + 7 T^{2} \))(\( 1 + T + 7 T^{2} \))(\( 1 - T + 7 T^{2} \))(\( 1 - T + 7 T^{2} \))
$11$ (\( 1 - 6 T + 23 T^{2} - 66 T^{3} + 121 T^{4} \))(\( 1 - 3 T + 14 T^{2} - 33 T^{3} + 121 T^{4} \))(\( 1 + 3 T + 14 T^{2} + 33 T^{3} + 121 T^{4} \))(\( 1 + 6 T + 23 T^{2} + 66 T^{3} + 121 T^{4} \))(\( 1 + 3 T + 14 T^{2} + 33 T^{3} + 121 T^{4} \))(\( 1 - 6 T + 23 T^{2} - 66 T^{3} + 121 T^{4} \))(\( 1 + 6 T + 23 T^{2} + 66 T^{3} + 121 T^{4} \))(\( 1 - 3 T + 14 T^{2} - 33 T^{3} + 121 T^{4} \))
$13$ (\( 1 + 13 T^{2} + 169 T^{4} \))(\( ( 1 + 2 T + 13 T^{2} )( 1 + 7 T + 13 T^{2} ) \))(\( ( 1 + 2 T + 13 T^{2} )( 1 + 7 T + 13 T^{2} ) \))(\( 1 + 13 T^{2} + 169 T^{4} \))(\( ( 1 - 7 T + 13 T^{2} )( 1 - 2 T + 13 T^{2} ) \))(\( 1 + 13 T^{2} + 169 T^{4} \))(\( 1 + 13 T^{2} + 169 T^{4} \))(\( ( 1 - 7 T + 13 T^{2} )( 1 - 2 T + 13 T^{2} ) \))
$17$ (\( 1 - 22 T^{2} + 289 T^{4} \))(\( 1 + 14 T^{2} + 289 T^{4} \))(\( 1 + 14 T^{2} + 289 T^{4} \))(\( 1 - 22 T^{2} + 289 T^{4} \))(\( 1 + 14 T^{2} + 289 T^{4} \))(\( 1 - 22 T^{2} + 289 T^{4} \))(\( 1 - 22 T^{2} + 289 T^{4} \))(\( 1 + 14 T^{2} + 289 T^{4} \))
$19$ (\( ( 1 + 5 T + 19 T^{2} )^{2} \))(\( ( 1 + 4 T + 19 T^{2} )^{2} \))(\( ( 1 - 4 T + 19 T^{2} )^{2} \))(\( ( 1 - 5 T + 19 T^{2} )^{2} \))(\( ( 1 + 4 T + 19 T^{2} )^{2} \))(\( ( 1 - 5 T + 19 T^{2} )^{2} \))(\( ( 1 + 5 T + 19 T^{2} )^{2} \))(\( ( 1 - 4 T + 19 T^{2} )^{2} \))
$23$ (\( 1 - 9 T + 50 T^{2} - 207 T^{3} + 529 T^{4} \))(\( 1 - 9 T + 50 T^{2} - 207 T^{3} + 529 T^{4} \))(\( 1 + 9 T + 50 T^{2} + 207 T^{3} + 529 T^{4} \))(\( 1 + 9 T + 50 T^{2} + 207 T^{3} + 529 T^{4} \))(\( 1 + 9 T + 50 T^{2} + 207 T^{3} + 529 T^{4} \))(\( 1 - 9 T + 50 T^{2} - 207 T^{3} + 529 T^{4} \))(\( 1 + 9 T + 50 T^{2} + 207 T^{3} + 529 T^{4} \))(\( 1 - 9 T + 50 T^{2} - 207 T^{3} + 529 T^{4} \))
$29$ (\( 1 - 29 T^{2} + 841 T^{4} \))(\( 1 + 9 T + 52 T^{2} + 261 T^{3} + 841 T^{4} \))(\( 1 + 9 T + 52 T^{2} + 261 T^{3} + 841 T^{4} \))(\( 1 - 29 T^{2} + 841 T^{4} \))(\( 1 + 9 T + 52 T^{2} + 261 T^{3} + 841 T^{4} \))(\( 1 - 29 T^{2} + 841 T^{4} \))(\( 1 - 29 T^{2} + 841 T^{4} \))(\( 1 + 9 T + 52 T^{2} + 261 T^{3} + 841 T^{4} \))
$31$ (\( 1 + 2 T - 27 T^{2} + 62 T^{3} + 961 T^{4} \))(\( ( 1 - 4 T + 31 T^{2} )( 1 + 11 T + 31 T^{2} ) \))(\( ( 1 - 11 T + 31 T^{2} )( 1 + 4 T + 31 T^{2} ) \))(\( 1 - 2 T - 27 T^{2} - 62 T^{3} + 961 T^{4} \))(\( ( 1 - 4 T + 31 T^{2} )( 1 + 11 T + 31 T^{2} ) \))(\( 1 - 2 T - 27 T^{2} - 62 T^{3} + 961 T^{4} \))(\( 1 + 2 T - 27 T^{2} + 62 T^{3} + 961 T^{4} \))(\( ( 1 - 11 T + 31 T^{2} )( 1 + 4 T + 31 T^{2} ) \))
$37$ (\( ( 1 + 8 T + 37 T^{2} )^{2} \))(\( ( 1 - 10 T + 37 T^{2} )^{2} \))(\( ( 1 - 10 T + 37 T^{2} )^{2} \))(\( ( 1 + 8 T + 37 T^{2} )^{2} \))(\( ( 1 - 10 T + 37 T^{2} )^{2} \))(\( ( 1 + 8 T + 37 T^{2} )^{2} \))(\( ( 1 + 8 T + 37 T^{2} )^{2} \))(\( ( 1 - 10 T + 37 T^{2} )^{2} \))
$41$ (\( 1 + 41 T^{2} + 1681 T^{4} \))(\( 1 - 9 T + 68 T^{2} - 369 T^{3} + 1681 T^{4} \))(\( 1 - 9 T + 68 T^{2} - 369 T^{3} + 1681 T^{4} \))(\( 1 + 41 T^{2} + 1681 T^{4} \))(\( 1 + 9 T + 68 T^{2} + 369 T^{3} + 1681 T^{4} \))(\( 1 + 41 T^{2} + 1681 T^{4} \))(\( 1 + 41 T^{2} + 1681 T^{4} \))(\( 1 + 9 T + 68 T^{2} + 369 T^{3} + 1681 T^{4} \))
$43$ (\( 1 - 6 T + 55 T^{2} - 258 T^{3} + 1849 T^{4} \))(\( 1 + 15 T + 118 T^{2} + 645 T^{3} + 1849 T^{4} \))(\( 1 - 15 T + 118 T^{2} - 645 T^{3} + 1849 T^{4} \))(\( 1 + 6 T + 55 T^{2} + 258 T^{3} + 1849 T^{4} \))(\( 1 - 15 T + 118 T^{2} - 645 T^{3} + 1849 T^{4} \))(\( 1 - 6 T + 55 T^{2} - 258 T^{3} + 1849 T^{4} \))(\( 1 + 6 T + 55 T^{2} + 258 T^{3} + 1849 T^{4} \))(\( 1 + 15 T + 118 T^{2} + 645 T^{3} + 1849 T^{4} \))
$47$ (\( 1 + 6 T - 11 T^{2} + 282 T^{3} + 2209 T^{4} \))(\( 1 + 3 T - 38 T^{2} + 141 T^{3} + 2209 T^{4} \))(\( 1 - 3 T - 38 T^{2} - 141 T^{3} + 2209 T^{4} \))(\( 1 - 6 T - 11 T^{2} - 282 T^{3} + 2209 T^{4} \))(\( 1 + 3 T - 38 T^{2} + 141 T^{3} + 2209 T^{4} \))(\( 1 - 6 T - 11 T^{2} - 282 T^{3} + 2209 T^{4} \))(\( 1 + 6 T - 11 T^{2} + 282 T^{3} + 2209 T^{4} \))(\( 1 - 3 T - 38 T^{2} - 141 T^{3} + 2209 T^{4} \))
$53$ (\( ( 1 - 6 T + 53 T^{2} )^{2} \))(\( ( 1 - 6 T + 53 T^{2} )^{2} \))(\( ( 1 - 6 T + 53 T^{2} )^{2} \))(\( ( 1 - 6 T + 53 T^{2} )^{2} \))(\( ( 1 - 6 T + 53 T^{2} )^{2} \))(\( ( 1 - 6 T + 53 T^{2} )^{2} \))(\( ( 1 - 6 T + 53 T^{2} )^{2} \))(\( ( 1 - 6 T + 53 T^{2} )^{2} \))
$59$ (\( 1 + 12 T + 85 T^{2} + 708 T^{3} + 3481 T^{4} \))(\( 1 - 3 T - 50 T^{2} - 177 T^{3} + 3481 T^{4} \))(\( 1 + 3 T - 50 T^{2} + 177 T^{3} + 3481 T^{4} \))(\( 1 - 12 T + 85 T^{2} - 708 T^{3} + 3481 T^{4} \))(\( 1 - 3 T - 50 T^{2} - 177 T^{3} + 3481 T^{4} \))(\( 1 - 12 T + 85 T^{2} - 708 T^{3} + 3481 T^{4} \))(\( 1 + 12 T + 85 T^{2} + 708 T^{3} + 3481 T^{4} \))(\( 1 + 3 T - 50 T^{2} + 177 T^{3} + 3481 T^{4} \))
$61$ (\( 1 - 3 T + 64 T^{2} - 183 T^{3} + 3721 T^{4} \))(\( 1 - 3 T + 64 T^{2} - 183 T^{3} + 3721 T^{4} \))(\( 1 - 3 T + 64 T^{2} - 183 T^{3} + 3721 T^{4} \))(\( 1 - 3 T + 64 T^{2} - 183 T^{3} + 3721 T^{4} \))(\( 1 + 3 T + 64 T^{2} + 183 T^{3} + 3721 T^{4} \))(\( 1 + 3 T + 64 T^{2} + 183 T^{3} + 3721 T^{4} \))(\( 1 + 3 T + 64 T^{2} + 183 T^{3} + 3721 T^{4} \))(\( 1 + 3 T + 64 T^{2} + 183 T^{3} + 3721 T^{4} \))
$67$ (\( 1 - 12 T + 115 T^{2} - 804 T^{3} + 4489 T^{4} \))(\( 1 - 15 T + 142 T^{2} - 1005 T^{3} + 4489 T^{4} \))(\( 1 + 15 T + 142 T^{2} + 1005 T^{3} + 4489 T^{4} \))(\( 1 + 12 T + 115 T^{2} + 804 T^{3} + 4489 T^{4} \))(\( 1 + 15 T + 142 T^{2} + 1005 T^{3} + 4489 T^{4} \))(\( 1 - 12 T + 115 T^{2} - 804 T^{3} + 4489 T^{4} \))(\( 1 + 12 T + 115 T^{2} + 804 T^{3} + 4489 T^{4} \))(\( 1 - 15 T + 142 T^{2} - 1005 T^{3} + 4489 T^{4} \))
$71$ (\( 1 + 5 T^{2} + 5041 T^{4} \))(\( 1 - 130 T^{2} + 5041 T^{4} \))(\( 1 - 130 T^{2} + 5041 T^{4} \))(\( 1 + 5 T^{2} + 5041 T^{4} \))(\( 1 - 130 T^{2} + 5041 T^{4} \))(\( 1 + 5 T^{2} + 5041 T^{4} \))(\( 1 + 5 T^{2} + 5041 T^{4} \))(\( 1 - 130 T^{2} + 5041 T^{4} \))
$73$ (\( 1 - 98 T^{2} + 5329 T^{4} \))(\( 1 - 98 T^{2} + 5329 T^{4} \))(\( 1 - 98 T^{2} + 5329 T^{4} \))(\( 1 - 98 T^{2} + 5329 T^{4} \))(\( 1 - 98 T^{2} + 5329 T^{4} \))(\( 1 - 98 T^{2} + 5329 T^{4} \))(\( 1 - 98 T^{2} + 5329 T^{4} \))(\( 1 - 98 T^{2} + 5329 T^{4} \))
$79$ (\( 1 + 27 T + 322 T^{2} + 2133 T^{3} + 6241 T^{4} \))(\( ( 1 - 13 T + 79 T^{2} )( 1 + 4 T + 79 T^{2} ) \))(\( ( 1 - 4 T + 79 T^{2} )( 1 + 13 T + 79 T^{2} ) \))(\( 1 - 27 T + 322 T^{2} - 2133 T^{3} + 6241 T^{4} \))(\( ( 1 - 4 T + 79 T^{2} )( 1 + 13 T + 79 T^{2} ) \))(\( 1 + 27 T + 322 T^{2} + 2133 T^{3} + 6241 T^{4} \))(\( 1 - 27 T + 322 T^{2} - 2133 T^{3} + 6241 T^{4} \))(\( ( 1 - 13 T + 79 T^{2} )( 1 + 4 T + 79 T^{2} ) \))
$83$ (\( 1 - 83 T^{2} + 6889 T^{4} \))(\( 1 - 9 T - 2 T^{2} - 747 T^{3} + 6889 T^{4} \))(\( 1 + 9 T - 2 T^{2} + 747 T^{3} + 6889 T^{4} \))(\( 1 - 83 T^{2} + 6889 T^{4} \))(\( 1 - 9 T - 2 T^{2} - 747 T^{3} + 6889 T^{4} \))(\( 1 - 83 T^{2} + 6889 T^{4} \))(\( 1 - 83 T^{2} + 6889 T^{4} \))(\( 1 + 9 T - 2 T^{2} + 747 T^{3} + 6889 T^{4} \))
$89$ (\( 1 + 14 T^{2} + 7921 T^{4} \))(\( 1 - 130 T^{2} + 7921 T^{4} \))(\( 1 - 130 T^{2} + 7921 T^{4} \))(\( 1 + 14 T^{2} + 7921 T^{4} \))(\( 1 - 130 T^{2} + 7921 T^{4} \))(\( 1 + 14 T^{2} + 7921 T^{4} \))(\( 1 + 14 T^{2} + 7921 T^{4} \))(\( 1 - 130 T^{2} + 7921 T^{4} \))
$97$ (\( 1 + 18 T + 205 T^{2} + 1746 T^{3} + 9409 T^{4} \))(\( ( 1 - 5 T + 97 T^{2} )( 1 + 14 T + 97 T^{2} ) \))(\( ( 1 - 5 T + 97 T^{2} )( 1 + 14 T + 97 T^{2} ) \))(\( 1 + 18 T + 205 T^{2} + 1746 T^{3} + 9409 T^{4} \))(\( ( 1 - 14 T + 97 T^{2} )( 1 + 5 T + 97 T^{2} ) \))(\( 1 - 18 T + 205 T^{2} - 1746 T^{3} + 9409 T^{4} \))(\( 1 - 18 T + 205 T^{2} - 1746 T^{3} + 9409 T^{4} \))(\( ( 1 - 14 T + 97 T^{2} )( 1 + 5 T + 97 T^{2} ) \))
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