Properties

Label 7524.2.l
Level 7524
Weight 2
Character orbit l
Rep. character \(\chi_{7524}(2089,\cdot)\)
Character field \(\Q\)
Dimension 100
Newform subspaces 6
Sturm bound 2880
Trace bound 25

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Defining parameters

Level: \( N \) \(=\) \( 7524 = 2^{2} \cdot 3^{2} \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7524.l (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 209 \)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(2880\)
Trace bound: \(25\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(7524, [\chi])\).

Total New Old
Modular forms 1464 100 1364
Cusp forms 1416 100 1316
Eisenstein series 48 0 48

Trace form

\( 100q + 2q^{5} + O(q^{10}) \) \( 100q + 2q^{5} - q^{11} + 8q^{23} + 106q^{25} - 2q^{47} - 78q^{49} - 5q^{55} + 53q^{77} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(7524, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
7524.2.l.a \(4\) \(60.079\) \(\Q(\sqrt{-3}, \sqrt{-19})\) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(2\) \(0\) \(q+(-\beta _{1}-\beta _{3})q^{5}+(-\beta _{1}-2\beta _{2}+\beta _{3})q^{7}+\cdots\)
7524.2.l.b \(8\) \(60.079\) 8.0.\(\cdots\).6 \(\Q(\sqrt{-627}) \) \(0\) \(0\) \(0\) \(0\) \(q-\beta _{6}q^{11}-\beta _{1}q^{13}+\beta _{3}q^{17}-\beta _{4}q^{19}+\cdots\)
7524.2.l.c \(8\) \(60.079\) 8.0.2702336256.1 \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{5}+\beta _{7})q^{5}+(\beta _{3}-\beta _{4})q^{7}+(\beta _{2}-\beta _{5}+\cdots)q^{11}+\cdots\)
7524.2.l.d \(16\) \(60.079\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(-4\) \(0\) \(q+\beta _{2}q^{5}+(\beta _{9}-\beta _{12})q^{7}+(-\beta _{3}-\beta _{9}+\cdots)q^{11}+\cdots\)
7524.2.l.e \(24\) \(60.079\) None \(0\) \(0\) \(0\) \(0\)
7524.2.l.f \(40\) \(60.079\) None \(0\) \(0\) \(4\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(7524, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(7524, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(209, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(418, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(627, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(836, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1254, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1881, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2508, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(3762, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ 1
$3$ 1
$5$ (\( ( 1 - T - 4 T^{2} - 5 T^{3} + 25 T^{4} )^{2} \))(\( ( 1 + 5 T^{2} )^{8} \))(\( ( 1 + 9 T^{2} + 56 T^{4} + 225 T^{6} + 625 T^{8} )^{2} \))(\( ( 1 + T + 14 T^{2} + 14 T^{3} + 93 T^{4} + 70 T^{5} + 350 T^{6} + 125 T^{7} + 625 T^{8} )^{4} \))
$7$ (\( ( 1 - 3 T + 2 T^{2} - 21 T^{3} + 49 T^{4} )( 1 + 3 T + 2 T^{2} + 21 T^{3} + 49 T^{4} ) \))(\( ( 1 - 7 T^{2} )^{8} \))(\( ( 1 - 3 T + 2 T^{2} - 21 T^{3} + 49 T^{4} )^{2}( 1 + 3 T + 2 T^{2} + 21 T^{3} + 49 T^{4} )^{2} \))(\( ( 1 - 27 T^{2} + 401 T^{4} - 4271 T^{6} + 34558 T^{8} - 209279 T^{10} + 962801 T^{12} - 3176523 T^{14} + 5764801 T^{16} )^{2} \))
$11$ (\( 1 - 5 T + 14 T^{2} - 55 T^{3} + 121 T^{4} \))(\( ( 1 + 11 T^{2} )^{4} \))(\( 1 - 3 T^{2} - 112 T^{4} - 363 T^{6} + 14641 T^{8} \))(\( ( 1 - 8 T^{2} - 16 T^{3} + 158 T^{4} - 176 T^{5} - 968 T^{6} + 14641 T^{8} )^{2} \))
$13$ (\( ( 1 + 13 T^{2} )^{4} \))(\( ( 1 - 7 T^{2} - 120 T^{4} - 1183 T^{6} + 28561 T^{8} )^{2} \))(\( ( 1 + 13 T^{2} )^{8} \))(\( ( 1 + 35 T^{2} + 835 T^{4} + 14799 T^{6} + 205786 T^{8} + 2501031 T^{10} + 23848435 T^{12} + 168938315 T^{14} + 815730721 T^{16} )^{2} \))
$17$ (\( ( 1 - 7 T + 32 T^{2} - 119 T^{3} + 289 T^{4} )( 1 + 7 T + 32 T^{2} + 119 T^{3} + 289 T^{4} ) \))(\( ( 1 + 23 T^{2} + 240 T^{4} + 6647 T^{6} + 83521 T^{8} )^{2} \))(\( ( 1 - 15 T^{2} - 64 T^{4} - 4335 T^{6} + 83521 T^{8} )^{2} \))(\( ( 1 - 68 T^{2} + 2562 T^{4} - 67908 T^{6} + 1329770 T^{8} - 19625412 T^{10} + 213980802 T^{12} - 1641354692 T^{14} + 6975757441 T^{16} )^{2} \))
$19$ (\( ( 1 + 19 T^{2} )^{2} \))(\( ( 1 - 19 T^{2} )^{4} \))(\( ( 1 + 19 T^{2} )^{4} \))(\( 1 - 72 T^{2} + 2596 T^{4} - 62296 T^{6} + 1241878 T^{8} - 22488856 T^{10} + 338313316 T^{12} - 3387303432 T^{14} + 16983563041 T^{16} \))
$23$ (\( ( 1 - 4 T + 23 T^{2} )^{4} \))(\( ( 1 + 23 T^{2} )^{8} \))(\( ( 1 - 30 T^{2} + 529 T^{4} )^{4} \))(\( ( 1 + 6 T + 31 T^{2} - 50 T^{3} - 208 T^{4} - 1150 T^{5} + 16399 T^{6} + 73002 T^{7} + 279841 T^{8} )^{4} \))
$29$ (\( ( 1 + 29 T^{2} )^{4} \))(\( ( 1 + 29 T^{2} )^{8} \))(\( ( 1 + 29 T^{2} )^{8} \))(\( ( 1 + 9 T^{2} + 2487 T^{4} + 14677 T^{6} + 2851658 T^{8} + 12343357 T^{10} + 1759007847 T^{12} + 5353409889 T^{14} + 500246412961 T^{16} )^{2} \))
$31$ (\( ( 1 - 31 T^{2} )^{4} \))(\( ( 1 - 31 T^{2} )^{8} \))(\( ( 1 - 31 T^{2} )^{8} \))(\( ( 1 - 103 T^{2} + 4002 T^{4} - 49206 T^{6} - 337155 T^{8} - 47286966 T^{10} + 3695931042 T^{12} - 91412879143 T^{14} + 852891037441 T^{16} )^{2} \))
$37$ (\( ( 1 - 37 T^{2} )^{4} \))(\( ( 1 - 37 T^{2} )^{8} \))(\( ( 1 - 37 T^{2} )^{8} \))(\( ( 1 - 210 T^{2} + 21323 T^{4} - 1365278 T^{6} + 60199048 T^{8} - 1869065582 T^{10} + 39962735003 T^{12} - 538802545890 T^{14} + 3512479453921 T^{16} )^{2} \))
$41$ (\( ( 1 + 41 T^{2} )^{4} \))(\( ( 1 + 41 T^{2} )^{8} \))(\( ( 1 + 41 T^{2} )^{8} \))(\( ( 1 + 87 T^{2} + 5553 T^{4} + 235189 T^{6} + 10743668 T^{8} + 395352709 T^{10} + 15691450833 T^{12} + 413259068967 T^{14} + 7984925229121 T^{16} )^{2} \))
$43$ (\( ( 1 - T - 42 T^{2} - 43 T^{3} + 1849 T^{4} )( 1 + T - 42 T^{2} + 43 T^{3} + 1849 T^{4} ) \))(\( ( 1 - 43 T^{2} )^{8} \))(\( ( 1 - T - 42 T^{2} - 43 T^{3} + 1849 T^{4} )^{2}( 1 + T - 42 T^{2} + 43 T^{3} + 1849 T^{4} )^{2} \))(\( ( 1 - 91 T^{2} + 3663 T^{4} - 229353 T^{6} + 13812624 T^{8} - 424073697 T^{10} + 12523068063 T^{12} - 575244037459 T^{14} + 11688200277601 T^{16} )^{2} \))
$47$ (\( ( 1 - 13 T + 122 T^{2} - 611 T^{3} + 2209 T^{4} )^{2} \))(\( ( 1 + 47 T^{2} )^{8} \))(\( ( 1 - 75 T^{2} + 3416 T^{4} - 165675 T^{6} + 4879681 T^{8} )^{2} \))(\( ( 1 + 130 T^{2} - 160 T^{3} + 7730 T^{4} - 7520 T^{5} + 287170 T^{6} + 4879681 T^{8} )^{4} \))
$53$ (\( ( 1 - 53 T^{2} )^{4} \))(\( ( 1 - 103 T^{2} + 7800 T^{4} - 289327 T^{6} + 7890481 T^{8} )^{2} \))(\( ( 1 - 53 T^{2} )^{8} \))(\( ( 1 - 200 T^{2} + 24072 T^{4} - 1954968 T^{6} + 119756942 T^{8} - 5491505112 T^{10} + 189939658632 T^{12} - 4432872225800 T^{14} + 62259690411361 T^{16} )^{2} \))
$59$ (\( ( 1 - 59 T^{2} )^{4} \))(\( ( 1 - 91 T^{2} + 4800 T^{4} - 316771 T^{6} + 12117361 T^{8} )^{2} \))(\( ( 1 - 59 T^{2} )^{8} \))(\( ( 1 - 170 T^{2} + 16291 T^{4} - 1174630 T^{6} + 72800408 T^{8} - 4088887030 T^{10} + 197403928051 T^{12} - 7170690718970 T^{14} + 146830437604321 T^{16} )^{2} \))
$61$ (\( ( 1 - 15 T + 164 T^{2} - 915 T^{3} + 3721 T^{4} )( 1 + 15 T + 164 T^{2} + 915 T^{3} + 3721 T^{4} ) \))(\( ( 1 - 61 T^{2} )^{8} \))(\( ( 1 - 15 T + 164 T^{2} - 915 T^{3} + 3721 T^{4} )^{2}( 1 + 15 T + 164 T^{2} + 915 T^{3} + 3721 T^{4} )^{2} \))(\( ( 1 - 284 T^{2} + 34578 T^{4} - 2519772 T^{6} + 151403786 T^{8} - 9376071612 T^{10} + 478761490098 T^{12} - 14631786318524 T^{14} + 191707312997281 T^{16} )^{2} \))
$67$ (\( ( 1 - 67 T^{2} )^{4} \))(\( ( 1 - 67 T^{2} )^{8} \))(\( ( 1 - 67 T^{2} )^{8} \))(\( ( 1 - 271 T^{2} + 44118 T^{4} - 4721574 T^{6} + 371643813 T^{8} - 21195145686 T^{10} + 889027156278 T^{12} - 24514221567799 T^{14} + 406067677556641 T^{16} )^{2} \))
$71$ (\( ( 1 - 71 T^{2} )^{4} \))(\( ( 1 - 67 T^{2} - 552 T^{4} - 337747 T^{6} + 25411681 T^{8} )^{2} \))(\( ( 1 - 71 T^{2} )^{8} \))(\( ( 1 - 297 T^{2} + 43322 T^{4} - 4385978 T^{6} + 347841481 T^{8} - 22109715098 T^{10} + 1100884844282 T^{12} - 38045784324537 T^{14} + 645753531245761 T^{16} )^{2} \))
$73$ (\( ( 1 - 11 T + 48 T^{2} - 803 T^{3} + 5329 T^{4} )( 1 + 11 T + 48 T^{2} + 803 T^{3} + 5329 T^{4} ) \))(\( ( 1 - 73 T^{2} )^{8} \))(\( ( 1 - 11 T + 48 T^{2} - 803 T^{3} + 5329 T^{4} )^{2}( 1 + 11 T + 48 T^{2} + 803 T^{3} + 5329 T^{4} )^{2} \))(\( ( 1 - 84 T^{2} + 15956 T^{4} - 1023404 T^{6} + 121082902 T^{8} - 5453719916 T^{10} + 453122333396 T^{12} - 12712075008276 T^{14} + 806460091894081 T^{16} )^{2} \))
$79$ (\( ( 1 + 79 T^{2} )^{4} \))(\( ( 1 - 139 T^{2} + 13080 T^{4} - 867499 T^{6} + 38950081 T^{8} )^{2} \))(\( ( 1 + 79 T^{2} )^{8} \))(\( ( 1 + 404 T^{2} + 79470 T^{4} + 10151916 T^{6} + 932638722 T^{8} + 63358107756 T^{10} + 3095362937070 T^{12} + 98207332030484 T^{14} + 1517108809906561 T^{16} )^{2} \))
$83$ (\( ( 1 - 16 T + 83 T^{2} )^{2}( 1 + 16 T + 83 T^{2} )^{2} \))(\( ( 1 - 109 T^{2} + 4992 T^{4} - 750901 T^{6} + 47458321 T^{8} )^{2} \))(\( ( 1 + 90 T^{2} + 6889 T^{4} )^{4} \))(\( ( 1 - 279 T^{2} + 48153 T^{4} - 5919251 T^{6} + 567786878 T^{8} - 40777720139 T^{10} + 2285260531113 T^{12} - 91216364169951 T^{14} + 2252292232139041 T^{16} )^{2} \))
$89$ (\( ( 1 - 89 T^{2} )^{4} \))(\( ( 1 - 31 T^{2} - 6960 T^{4} - 245551 T^{6} + 62742241 T^{8} )^{2} \))(\( ( 1 - 89 T^{2} )^{8} \))(\( ( 1 - 378 T^{2} + 61403 T^{4} - 6095438 T^{6} + 519716488 T^{8} - 48281964398 T^{10} + 3852561824123 T^{12} - 187858927983258 T^{14} + 3936588805702081 T^{16} )^{2} \))
$97$ (\( ( 1 - 97 T^{2} )^{4} \))(\( ( 1 - 97 T^{2} )^{8} \))(\( ( 1 - 97 T^{2} )^{8} \))(\( ( 1 - 358 T^{2} + 74235 T^{4} - 10905078 T^{6} + 1222175376 T^{8} - 102605878902 T^{10} + 6571971175035 T^{12} - 298203977764582 T^{14} + 7837433594376961 T^{16} )^{2} \))
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