Properties

Label 3024.2.bf
Level 3024
Weight 2
Character orbit bf
Rep. character \(\chi_{3024}(1711,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 96
Newform subspaces 9
Sturm bound 1152
Trace bound 7

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Defining parameters

Level: \( N \) = \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3024.bf (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 252 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 9 \)
Sturm bound: \(1152\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(19\)

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

\( 96q + O(q^{10}) \) \( 96q - 96q^{25} + 12q^{29} - 24q^{65} + 24q^{77} - 36q^{89} + O(q^{100}) \)

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.bf.a \(2\) \(24.147\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-5\) \(q+(1-2\zeta_{6})q^{5}+(-3+\zeta_{6})q^{7}+(3-6\zeta_{6})q^{11}+\cdots\)
3024.2.bf.b \(2\) \(24.147\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-4\) \(q+(-1-2\zeta_{6})q^{7}+(-2+4\zeta_{6})q^{11}+\cdots\)
3024.2.bf.c \(2\) \(24.147\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(4\) \(q+(1+2\zeta_{6})q^{7}+(2-4\zeta_{6})q^{11}+(1+\zeta_{6})q^{13}+\cdots\)
3024.2.bf.d \(2\) \(24.147\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(5\) \(q+(1-2\zeta_{6})q^{5}+(3-\zeta_{6})q^{7}+(-3+6\zeta_{6})q^{11}+\cdots\)
3024.2.bf.e \(4\) \(24.147\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(-2\) \(q+(1+2\beta _{1}-\beta _{2})q^{5}+(\beta _{1}+\beta _{3})q^{7}+\cdots\)
3024.2.bf.f \(4\) \(24.147\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(2\) \(q+(1+2\beta _{1}-\beta _{2})q^{5}+(-\beta _{1}-\beta _{3})q^{7}+\cdots\)
3024.2.bf.g \(24\) \(24.147\) None \(0\) \(0\) \(0\) \(-8\)
3024.2.bf.h \(24\) \(24.147\) None \(0\) \(0\) \(0\) \(8\)
3024.2.bf.i \(32\) \(24.147\) 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
$5$ (\( 1 - 7 T^{2} + 25 T^{4} \))(\( ( 1 - 5 T^{2} )^{2} \))(\( ( 1 - 5 T^{2} )^{2} \))(\( 1 - 7 T^{2} + 25 T^{4} \))(\( ( 1 - 6 T + 17 T^{2} - 30 T^{3} + 25 T^{4} )( 1 + 6 T + 17 T^{2} + 30 T^{3} + 25 T^{4} ) \))(\( ( 1 - 6 T + 17 T^{2} - 30 T^{3} + 25 T^{4} )( 1 + 6 T + 17 T^{2} + 30 T^{3} + 25 T^{4} ) \))
$7$ (\( 1 + 5 T + 7 T^{2} \))(\( 1 + 4 T + 7 T^{2} \))(\( 1 - 4 T + 7 T^{2} \))(\( 1 - 5 T + 7 T^{2} \))(\( 1 + 2 T - 3 T^{2} + 14 T^{3} + 49 T^{4} \))(\( 1 - 2 T - 3 T^{2} - 14 T^{3} + 49 T^{4} \))
$11$ (\( 1 + 5 T^{2} + 121 T^{4} \))(\( 1 - 10 T^{2} + 121 T^{4} \))(\( 1 - 10 T^{2} + 121 T^{4} \))(\( 1 + 5 T^{2} + 121 T^{4} \))(\( ( 1 - 19 T^{2} + 121 T^{4} )^{2} \))(\( ( 1 - 19 T^{2} + 121 T^{4} )^{2} \))
$13$ (\( ( 1 + 2 T + 13 T^{2} )( 1 + 7 T + 13 T^{2} ) \))(\( ( 1 - 5 T + 13 T^{2} )( 1 + 2 T + 13 T^{2} ) \))(\( ( 1 - 5 T + 13 T^{2} )( 1 + 2 T + 13 T^{2} ) \))(\( ( 1 + 2 T + 13 T^{2} )( 1 + 7 T + 13 T^{2} ) \))(\( 1 - 6 T + 35 T^{2} - 138 T^{3} + 516 T^{4} - 1794 T^{5} + 5915 T^{6} - 13182 T^{7} + 28561 T^{8} \))(\( 1 - 6 T + 35 T^{2} - 138 T^{3} + 516 T^{4} - 1794 T^{5} + 5915 T^{6} - 13182 T^{7} + 28561 T^{8} \))
$17$ (\( 1 + 3 T + 20 T^{2} + 51 T^{3} + 289 T^{4} \))(\( 1 + 3 T + 20 T^{2} + 51 T^{3} + 289 T^{4} \))(\( 1 + 3 T + 20 T^{2} + 51 T^{3} + 289 T^{4} \))(\( 1 + 3 T + 20 T^{2} + 51 T^{3} + 289 T^{4} \))(\( 1 + 6 T + 25 T^{2} + 78 T^{3} + 84 T^{4} + 1326 T^{5} + 7225 T^{6} + 29478 T^{7} + 83521 T^{8} \))(\( 1 + 6 T + 25 T^{2} + 78 T^{3} + 84 T^{4} + 1326 T^{5} + 7225 T^{6} + 29478 T^{7} + 83521 T^{8} \))
$19$ (\( ( 1 - 7 T + 19 T^{2} )( 1 + 8 T + 19 T^{2} ) \))(\( 1 + 5 T + 6 T^{2} + 95 T^{3} + 361 T^{4} \))(\( 1 - 5 T + 6 T^{2} - 95 T^{3} + 361 T^{4} \))(\( ( 1 - 8 T + 19 T^{2} )( 1 + 7 T + 19 T^{2} ) \))(\( ( 1 - 8 T + 19 T^{2} )^{2}( 1 + 7 T + 19 T^{2} )^{2} \))(\( ( 1 - 7 T + 19 T^{2} )^{2}( 1 + 8 T + 19 T^{2} )^{2} \))
$23$ (\( 1 - 43 T^{2} + 529 T^{4} \))(\( 1 - 34 T^{2} + 529 T^{4} \))(\( 1 - 34 T^{2} + 529 T^{4} \))(\( 1 - 43 T^{2} + 529 T^{4} \))(\( 1 - 26 T^{2} + 579 T^{4} - 13754 T^{6} + 279841 T^{8} \))(\( 1 - 26 T^{2} + 579 T^{4} - 13754 T^{6} + 279841 T^{8} \))
$29$ (\( 1 - 9 T + 52 T^{2} - 261 T^{3} + 841 T^{4} \))(\( 1 - 3 T - 20 T^{2} - 87 T^{3} + 841 T^{4} \))(\( 1 - 3 T - 20 T^{2} - 87 T^{3} + 841 T^{4} \))(\( 1 - 9 T + 52 T^{2} - 261 T^{3} + 841 T^{4} \))(\( 1 - 6 T - 13 T^{2} + 54 T^{3} + 516 T^{4} + 1566 T^{5} - 10933 T^{6} - 146334 T^{7} + 707281 T^{8} \))(\( 1 - 6 T - 13 T^{2} + 54 T^{3} + 516 T^{4} + 1566 T^{5} - 10933 T^{6} - 146334 T^{7} + 707281 T^{8} \))
$31$ (\( 1 + 8 T + 33 T^{2} + 248 T^{3} + 961 T^{4} \))(\( 1 + T - 30 T^{2} + 31 T^{3} + 961 T^{4} \))(\( 1 - T - 30 T^{2} - 31 T^{3} + 961 T^{4} \))(\( 1 - 8 T + 33 T^{2} - 248 T^{3} + 961 T^{4} \))(\( ( 1 - 7 T + 31 T^{2} )^{2}( 1 + 11 T + 31 T^{2} )^{2} \))(\( ( 1 - 11 T + 31 T^{2} )^{2}( 1 + 7 T + 31 T^{2} )^{2} \))
$37$ (\( ( 1 - 10 T + 37 T^{2} )( 1 - T + 37 T^{2} ) \))(\( 1 + 7 T + 12 T^{2} + 259 T^{3} + 1369 T^{4} \))(\( 1 + 7 T + 12 T^{2} + 259 T^{3} + 1369 T^{4} \))(\( ( 1 - 10 T + 37 T^{2} )( 1 - T + 37 T^{2} ) \))(\( 1 + 2 T - 53 T^{2} - 34 T^{3} + 1732 T^{4} - 1258 T^{5} - 72557 T^{6} + 101306 T^{7} + 1874161 T^{8} \))(\( 1 + 2 T - 53 T^{2} - 34 T^{3} + 1732 T^{4} - 1258 T^{5} - 72557 T^{6} + 101306 T^{7} + 1874161 T^{8} \))
$41$ (\( 1 - 3 T + 44 T^{2} - 123 T^{3} + 1681 T^{4} \))(\( 1 + 3 T + 44 T^{2} + 123 T^{3} + 1681 T^{4} \))(\( 1 + 3 T + 44 T^{2} + 123 T^{3} + 1681 T^{4} \))(\( 1 - 3 T + 44 T^{2} - 123 T^{3} + 1681 T^{4} \))(\( 1 + 18 T + 193 T^{2} + 1530 T^{3} + 9972 T^{4} + 62730 T^{5} + 324433 T^{6} + 1240578 T^{7} + 2825761 T^{8} \))(\( 1 + 18 T + 193 T^{2} + 1530 T^{3} + 9972 T^{4} + 62730 T^{5} + 324433 T^{6} + 1240578 T^{7} + 2825761 T^{8} \))
$43$ (\( 1 + 15 T + 118 T^{2} + 645 T^{3} + 1849 T^{4} \))(\( ( 1 - 5 T + 43 T^{2} )( 1 + 8 T + 43 T^{2} ) \))(\( ( 1 - 8 T + 43 T^{2} )( 1 + 5 T + 43 T^{2} ) \))(\( 1 - 15 T + 118 T^{2} - 645 T^{3} + 1849 T^{4} \))(\( 1 + 6 T + 77 T^{2} + 390 T^{3} + 2892 T^{4} + 16770 T^{5} + 142373 T^{6} + 477042 T^{7} + 3418801 T^{8} \))(\( 1 - 6 T + 77 T^{2} - 390 T^{3} + 2892 T^{4} - 16770 T^{5} + 142373 T^{6} - 477042 T^{7} + 3418801 T^{8} \))
$47$ (\( 1 + 12 T + 97 T^{2} + 564 T^{3} + 2209 T^{4} \))(\( 1 + 9 T + 34 T^{2} + 423 T^{3} + 2209 T^{4} \))(\( 1 - 9 T + 34 T^{2} - 423 T^{3} + 2209 T^{4} \))(\( 1 - 12 T + 97 T^{2} - 564 T^{3} + 2209 T^{4} \))(\( 1 - 22 T^{2} - 1725 T^{4} - 48598 T^{6} + 4879681 T^{8} \))(\( 1 - 22 T^{2} - 1725 T^{4} - 48598 T^{6} + 4879681 T^{8} \))
$53$ (\( 1 + 3 T - 44 T^{2} + 159 T^{3} + 2809 T^{4} \))(\( 1 + 9 T + 28 T^{2} + 477 T^{3} + 2809 T^{4} \))(\( 1 + 9 T + 28 T^{2} + 477 T^{3} + 2809 T^{4} \))(\( 1 + 3 T - 44 T^{2} + 159 T^{3} + 2809 T^{4} \))(\( 1 + 6 T - 61 T^{2} - 54 T^{3} + 4692 T^{4} - 2862 T^{5} - 171349 T^{6} + 893262 T^{7} + 7890481 T^{8} \))(\( 1 + 6 T - 61 T^{2} - 54 T^{3} + 4692 T^{4} - 2862 T^{5} - 171349 T^{6} + 893262 T^{7} + 7890481 T^{8} \))
$59$ (\( 1 - 12 T + 85 T^{2} - 708 T^{3} + 3481 T^{4} \))(\( 1 + 15 T + 166 T^{2} + 885 T^{3} + 3481 T^{4} \))(\( 1 - 15 T + 166 T^{2} - 885 T^{3} + 3481 T^{4} \))(\( 1 + 12 T + 85 T^{2} + 708 T^{3} + 3481 T^{4} \))(\( ( 1 - 6 T - 23 T^{2} - 354 T^{3} + 3481 T^{4} )^{2} \))(\( ( 1 + 6 T - 23 T^{2} + 354 T^{3} + 3481 T^{4} )^{2} \))
$61$ (\( 1 + 61 T^{2} + 3721 T^{4} \))(\( 1 - 3 T + 64 T^{2} - 183 T^{3} + 3721 T^{4} \))(\( 1 - 3 T + 64 T^{2} - 183 T^{3} + 3721 T^{4} \))(\( 1 + 61 T^{2} + 3721 T^{4} \))(\( ( 1 - 13 T + 61 T^{2} )^{2}( 1 + T + 61 T^{2} )^{2} \))(\( ( 1 - 13 T + 61 T^{2} )^{2}( 1 + T + 61 T^{2} )^{2} \))
$67$ (\( ( 1 - 11 T + 67 T^{2} )( 1 + 5 T + 67 T^{2} ) \))(\( ( 1 + 11 T + 67 T^{2} )( 1 + 16 T + 67 T^{2} ) \))(\( ( 1 - 16 T + 67 T^{2} )( 1 - 11 T + 67 T^{2} ) \))(\( ( 1 - 5 T + 67 T^{2} )( 1 + 11 T + 67 T^{2} ) \))(\( ( 1 + 67 T^{2} + 4489 T^{4} )^{2} \))(\( ( 1 + 67 T^{2} + 4489 T^{4} )^{2} \))
$71$ (\( 1 - 130 T^{2} + 5041 T^{4} \))(\( 1 - 34 T^{2} + 5041 T^{4} \))(\( 1 - 34 T^{2} + 5041 T^{4} \))(\( 1 - 130 T^{2} + 5041 T^{4} \))(\( 1 - 68 T^{2} + 6630 T^{4} - 342788 T^{6} + 25411681 T^{8} \))(\( 1 - 68 T^{2} + 6630 T^{4} - 342788 T^{6} + 25411681 T^{8} \))
$73$ (\( 1 + 21 T + 220 T^{2} + 1533 T^{3} + 5329 T^{4} \))(\( ( 1 - 10 T + 73 T^{2} )( 1 + 7 T + 73 T^{2} ) \))(\( ( 1 - 10 T + 73 T^{2} )( 1 + 7 T + 73 T^{2} ) \))(\( 1 + 21 T + 220 T^{2} + 1533 T^{3} + 5329 T^{4} \))(\( ( 1 + 15 T + 148 T^{2} + 1095 T^{3} + 5329 T^{4} )^{2} \))(\( ( 1 + 15 T + 148 T^{2} + 1095 T^{3} + 5329 T^{4} )^{2} \))
$79$ (\( 1 + 18 T + 187 T^{2} + 1422 T^{3} + 6241 T^{4} \))(\( 1 - 3 T + 82 T^{2} - 237 T^{3} + 6241 T^{4} \))(\( 1 + 3 T + 82 T^{2} + 237 T^{3} + 6241 T^{4} \))(\( 1 - 18 T + 187 T^{2} - 1422 T^{3} + 6241 T^{4} \))(\( 1 - 24 T + 374 T^{2} - 4368 T^{3} + 42051 T^{4} - 345072 T^{5} + 2334134 T^{6} - 11832936 T^{7} + 38950081 T^{8} \))(\( 1 + 24 T + 374 T^{2} + 4368 T^{3} + 42051 T^{4} + 345072 T^{5} + 2334134 T^{6} + 11832936 T^{7} + 38950081 T^{8} \))
$83$ (\( 1 + 9 T - 2 T^{2} + 747 T^{3} + 6889 T^{4} \))(\( 1 - 9 T - 2 T^{2} - 747 T^{3} + 6889 T^{4} \))(\( 1 + 9 T - 2 T^{2} + 747 T^{3} + 6889 T^{4} \))(\( 1 - 9 T - 2 T^{2} - 747 T^{3} + 6889 T^{4} \))(\( 1 - 6 T - 67 T^{2} + 378 T^{3} + 732 T^{4} + 31374 T^{5} - 461563 T^{6} - 3430722 T^{7} + 47458321 T^{8} \))(\( 1 + 6 T - 67 T^{2} - 378 T^{3} + 732 T^{4} - 31374 T^{5} - 461563 T^{6} + 3430722 T^{7} + 47458321 T^{8} \))
$89$ (\( 1 - 9 T + 116 T^{2} - 801 T^{3} + 7921 T^{4} \))(\( 1 + 3 T + 92 T^{2} + 267 T^{3} + 7921 T^{4} \))(\( 1 + 3 T + 92 T^{2} + 267 T^{3} + 7921 T^{4} \))(\( 1 - 9 T + 116 T^{2} - 801 T^{3} + 7921 T^{4} \))(\( 1 - 6 T - 23 T^{2} + 210 T^{3} - 5628 T^{4} + 18690 T^{5} - 182183 T^{6} - 4229814 T^{7} + 62742241 T^{8} \))(\( 1 - 6 T - 23 T^{2} + 210 T^{3} - 5628 T^{4} + 18690 T^{5} - 182183 T^{6} - 4229814 T^{7} + 62742241 T^{8} \))
$97$ (\( 1 + 3 T + 100 T^{2} + 291 T^{3} + 9409 T^{4} \))(\( 1 - 3 T + 100 T^{2} - 291 T^{3} + 9409 T^{4} \))(\( 1 - 3 T + 100 T^{2} - 291 T^{3} + 9409 T^{4} \))(\( 1 + 3 T + 100 T^{2} + 291 T^{3} + 9409 T^{4} \))(\( 1 - 6 T + 185 T^{2} - 1038 T^{3} + 21684 T^{4} - 100686 T^{5} + 1740665 T^{6} - 5476038 T^{7} + 88529281 T^{8} \))(\( 1 - 6 T + 185 T^{2} - 1038 T^{3} + 21684 T^{4} - 100686 T^{5} + 1740665 T^{6} - 5476038 T^{7} + 88529281 T^{8} \))
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