Properties

Label 8015.2
Level 8015
Weight 2
Dimension 2204331
Nonzero newspaces 100
Sturm bound 10068480

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Defining parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 100 \)
Sturm bound: \(10068480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8015))\).

Total New Old
Modular forms 2528064 2217947 310117
Cusp forms 2506177 2204331 301846
Eisenstein series 21887 13616 8271

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8015))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
8015.2.a \(\chi_{8015}(1, \cdot)\) 8015.2.a.a 1 1
8015.2.a.b 1
8015.2.a.c 1
8015.2.a.d 1
8015.2.a.e 1
8015.2.a.f 1
8015.2.a.g 3
8015.2.a.h 38
8015.2.a.i 44
8015.2.a.j 45
8015.2.a.k 49
8015.2.a.l 62
8015.2.a.m 67
8015.2.a.n 68
8015.2.a.o 73
8015.2.b \(\chi_{8015}(1604, \cdot)\) n/a 684 1
8015.2.d \(\chi_{8015}(2976, \cdot)\) n/a 460 1
8015.2.g \(\chi_{8015}(4579, \cdot)\) n/a 692 1
8015.2.i \(\chi_{8015}(781, \cdot)\) n/a 1228 2
8015.2.j \(\chi_{8015}(2291, \cdot)\) n/a 1216 2
8015.2.k \(\chi_{8015}(4216, \cdot)\) n/a 1228 2
8015.2.l \(\chi_{8015}(1926, \cdot)\) n/a 920 2
8015.2.n \(\chi_{8015}(1023, \cdot)\) n/a 1380 2
8015.2.o \(\chi_{8015}(3786, \cdot)\) n/a 1232 2
8015.2.r \(\chi_{8015}(1833, \cdot)\) n/a 1824 2
8015.2.t \(\chi_{8015}(1602, \cdot)\) n/a 1832 2
8015.2.u \(\chi_{8015}(5389, \cdot)\) n/a 1832 2
8015.2.w \(\chi_{8015}(5832, \cdot)\) n/a 1380 2
8015.2.y \(\chi_{8015}(1051, \cdot)\) n/a 920 2
8015.2.ba \(\chi_{8015}(134, \cdot)\) n/a 1376 2
8015.2.bd \(\chi_{8015}(4904, \cdot)\) n/a 1832 2
8015.2.bh \(\chi_{8015}(3434, \cdot)\) n/a 1832 2
8015.2.bj \(\chi_{8015}(324, \cdot)\) n/a 1832 2
8015.2.bl \(\chi_{8015}(5819, \cdot)\) n/a 1832 2
8015.2.bn \(\chi_{8015}(1831, \cdot)\) n/a 1224 2
8015.2.bp \(\chi_{8015}(6736, \cdot)\) n/a 1228 2
8015.2.br \(\chi_{8015}(2384, \cdot)\) n/a 1832 2
8015.2.bt \(\chi_{8015}(459, \cdot)\) n/a 1824 2
8015.2.bv \(\chi_{8015}(3301, \cdot)\) n/a 1228 2
8015.2.bz \(\chi_{8015}(2654, \cdot)\) n/a 1384 2
8015.2.cb \(\chi_{8015}(547, \cdot)\) n/a 2760 4
8015.2.cc \(\chi_{8015}(2608, \cdot)\) n/a 3664 4
8015.2.ce \(\chi_{8015}(18, \cdot)\) n/a 3664 4
8015.2.cf \(\chi_{8015}(107, \cdot)\) n/a 3664 4
8015.2.ci \(\chi_{8015}(1356, \cdot)\) n/a 2456 4
8015.2.cl \(\chi_{8015}(2379, \cdot)\) n/a 3664 4
8015.2.cn \(\chi_{8015}(89, \cdot)\) n/a 3664 4
8015.2.cp \(\chi_{8015}(794, \cdot)\) n/a 3664 4
8015.2.cq \(\chi_{8015}(2883, \cdot)\) n/a 3664 4
8015.2.cs \(\chi_{8015}(363, \cdot)\) n/a 3664 4
8015.2.cu \(\chi_{8015}(2978, \cdot)\) n/a 3648 4
8015.2.cx \(\chi_{8015}(593, \cdot)\) n/a 3664 4
8015.2.cy \(\chi_{8015}(782, \cdot)\) n/a 3664 4
8015.2.db \(\chi_{8015}(1468, \cdot)\) n/a 3664 4
8015.2.dc \(\chi_{8015}(1697, \cdot)\) n/a 3664 4
8015.2.de \(\chi_{8015}(2518, \cdot)\) n/a 3664 4
8015.2.dh \(\chi_{8015}(776, \cdot)\) n/a 2448 4
8015.2.dj \(\chi_{8015}(1496, \cdot)\) n/a 2448 4
8015.2.dl \(\chi_{8015}(4791, \cdot)\) n/a 2456 4
8015.2.dm \(\chi_{8015}(2959, \cdot)\) n/a 3664 4
8015.2.dp \(\chi_{8015}(247, \cdot)\) n/a 3664 4
8015.2.ds \(\chi_{8015}(2412, \cdot)\) n/a 3664 4
8015.2.dt \(\chi_{8015}(2837, \cdot)\) n/a 3664 4
8015.2.du \(\chi_{8015}(827, \cdot)\) n/a 2760 4
8015.2.dw \(\chi_{8015}(246, \cdot)\) n/a 8280 18
8015.2.dy \(\chi_{8015}(64, \cdot)\) n/a 12456 18
8015.2.eb \(\chi_{8015}(176, \cdot)\) n/a 8280 18
8015.2.ed \(\chi_{8015}(519, \cdot)\) n/a 12384 18
8015.2.ee \(\chi_{8015}(631, \cdot)\) n/a 16560 36
8015.2.ef \(\chi_{8015}(81, \cdot)\) n/a 22104 36
8015.2.eg \(\chi_{8015}(16, \cdot)\) n/a 22032 36
8015.2.eh \(\chi_{8015}(51, \cdot)\) n/a 22104 36
8015.2.ej \(\chi_{8015}(22, \cdot)\) n/a 24840 36
8015.2.el \(\chi_{8015}(34, \cdot)\) n/a 32976 36
8015.2.em \(\chi_{8015}(202, \cdot)\) n/a 32976 36
8015.2.eo \(\chi_{8015}(27, \cdot)\) n/a 32976 36
8015.2.er \(\chi_{8015}(216, \cdot)\) n/a 22176 36
8015.2.es \(\chi_{8015}(8, \cdot)\) n/a 24840 36
8015.2.eu \(\chi_{8015}(99, \cdot)\) n/a 24912 36
8015.2.ey \(\chi_{8015}(46, \cdot)\) n/a 22104 36
8015.2.fa \(\chi_{8015}(44, \cdot)\) n/a 32976 36
8015.2.fc \(\chi_{8015}(144, \cdot)\) n/a 32976 36
8015.2.fe \(\chi_{8015}(226, \cdot)\) n/a 22104 36
8015.2.fg \(\chi_{8015}(11, \cdot)\) n/a 22032 36
8015.2.fi \(\chi_{8015}(9, \cdot)\) n/a 32976 36
8015.2.fk \(\chi_{8015}(494, \cdot)\) n/a 32976 36
8015.2.fm \(\chi_{8015}(4, \cdot)\) n/a 32976 36
8015.2.fq \(\chi_{8015}(534, \cdot)\) n/a 32976 36
8015.2.ft \(\chi_{8015}(904, \cdot)\) n/a 24768 36
8015.2.fv \(\chi_{8015}(36, \cdot)\) n/a 16560 36
8015.2.fx \(\chi_{8015}(92, \cdot)\) n/a 49680 72
8015.2.fy \(\chi_{8015}(2, \cdot)\) n/a 65952 72
8015.2.fz \(\chi_{8015}(408, \cdot)\) n/a 65952 72
8015.2.gc \(\chi_{8015}(102, \cdot)\) n/a 65952 72
8015.2.gf \(\chi_{8015}(24, \cdot)\) n/a 65952 72
8015.2.gg \(\chi_{8015}(31, \cdot)\) n/a 44208 72
8015.2.gi \(\chi_{8015}(101, \cdot)\) n/a 44064 72
8015.2.gk \(\chi_{8015}(6, \cdot)\) n/a 44064 72
8015.2.gn \(\chi_{8015}(68, \cdot)\) n/a 65952 72
8015.2.gp \(\chi_{8015}(248, \cdot)\) n/a 65952 72
8015.2.gq \(\chi_{8015}(3, \cdot)\) n/a 65952 72
8015.2.gt \(\chi_{8015}(12, \cdot)\) n/a 65952 72
8015.2.gu \(\chi_{8015}(138, \cdot)\) n/a 65952 72
8015.2.gx \(\chi_{8015}(17, \cdot)\) n/a 65952 72
8015.2.gz \(\chi_{8015}(48, \cdot)\) n/a 65952 72
8015.2.hb \(\chi_{8015}(62, \cdot)\) n/a 65952 72
8015.2.hc \(\chi_{8015}(54, \cdot)\) n/a 65952 72
8015.2.he \(\chi_{8015}(59, \cdot)\) n/a 65952 72
8015.2.hg \(\chi_{8015}(69, \cdot)\) n/a 65952 72
8015.2.hj \(\chi_{8015}(66, \cdot)\) n/a 44208 72
8015.2.hm \(\chi_{8015}(23, \cdot)\) n/a 65952 72
8015.2.hn \(\chi_{8015}(88, \cdot)\) n/a 65952 72
8015.2.hp \(\chi_{8015}(67, \cdot)\) n/a 65952 72
8015.2.hq \(\chi_{8015}(162, \cdot)\) n/a 49680 72

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8015))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8015)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(229))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1145))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1603))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + 2 T + 2 T^{2} \))(\( 1 + T + 2 T^{2} \))(\( 1 + T + 2 T^{2} \))(\( 1 - T + 2 T^{2} \))(\( 1 - T + 2 T^{2} \))(\( 1 - 2 T + 2 T^{2} \))(\( 1 - T + 3 T^{2} - 3 T^{3} + 6 T^{4} - 4 T^{5} + 8 T^{6} \))
$3$ (\( 1 + 3 T + 3 T^{2} \))(\( 1 + 2 T + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( 1 - T + 3 T^{2} \))(\( 1 + T - 7 T^{3} + 9 T^{5} + 27 T^{6} \))
$5$ (\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( ( 1 + T )^{3} \))
$7$ (\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 - T \))(\( 1 + T \))(\( 1 - T \))(\( ( 1 + T )^{3} \))
$11$ (\( 1 - 5 T + 11 T^{2} \))(\( 1 - 3 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 4 T + 11 T^{2} \))(\( 1 + T + 11 T^{2} \))(\( 1 + 3 T + 11 T^{2} \))(\( 1 + 4 T + 29 T^{2} + 68 T^{3} + 319 T^{4} + 484 T^{5} + 1331 T^{6} \))
$13$ (\( 1 + T + 13 T^{2} \))(\( 1 + 7 T + 13 T^{2} \))(\( 1 - 5 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))(\( 1 + 5 T + 13 T^{2} \))(\( 1 - 3 T + 13 T^{2} \))(\( 1 + 3 T + 8 T^{2} - 17 T^{3} + 104 T^{4} + 507 T^{5} + 2197 T^{6} \))
$17$ (\( 1 - 3 T + 17 T^{2} \))(\( 1 - 6 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 6 T + 17 T^{2} \))(\( 1 - 2 T + 17 T^{2} \))(\( 1 + T + 17 T^{2} \))(\( 1 + 4 T + 43 T^{2} + 120 T^{3} + 731 T^{4} + 1156 T^{5} + 4913 T^{6} \))
$19$ (\( 1 - 2 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 8 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 - 4 T + 19 T^{2} \))(\( 1 + 6 T + 19 T^{2} \))(\( ( 1 + 19 T^{2} )^{3} \))
$23$ (\( 1 - 6 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 - 6 T + 23 T^{2} \))(\( 1 + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))(\( 1 + 2 T + 23 T^{2} \))(\( 1 + 4 T + 29 T^{2} + 116 T^{3} + 667 T^{4} + 2116 T^{5} + 12167 T^{6} \))
$29$ (\( 1 - 5 T + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 29 T^{2} \))(\( 1 + 10 T + 29 T^{2} \))(\( 1 + 4 T + 29 T^{2} \))(\( 1 + 3 T + 29 T^{2} \))(\( 1 - 10 T + 111 T^{2} - 576 T^{3} + 3219 T^{4} - 8410 T^{5} + 24389 T^{6} \))
$31$ (\( 1 - 2 T + 31 T^{2} \))(\( 1 + 9 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( 1 - 9 T + 31 T^{2} \))(\( 1 + 2 T + 31 T^{2} \))(\( 1 - 6 T + 21 T^{2} + 56 T^{3} + 651 T^{4} - 5766 T^{5} + 29791 T^{6} \))
$37$ (\( 1 + 8 T + 37 T^{2} \))(\( 1 + T + 37 T^{2} \))(\( 1 - 2 T + 37 T^{2} \))(\( 1 + 2 T + 37 T^{2} \))(\( 1 - 7 T + 37 T^{2} \))(\( 1 + 4 T + 37 T^{2} \))(\( 1 + 6 T + 75 T^{2} + 336 T^{3} + 2775 T^{4} + 8214 T^{5} + 50653 T^{6} \))
$41$ (\( 1 - 6 T + 41 T^{2} \))(\( 1 + 5 T + 41 T^{2} \))(\( 1 + 8 T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 - T + 41 T^{2} \))(\( 1 + 6 T + 41 T^{2} \))(\( 1 + 26 T + 339 T^{2} + 2712 T^{3} + 13899 T^{4} + 43706 T^{5} + 68921 T^{6} \))
$43$ (\( 1 + 4 T + 43 T^{2} \))(\( 1 - T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 - 8 T + 43 T^{2} \))(\( 1 + 3 T + 43 T^{2} \))(\( 1 + 8 T + 43 T^{2} \))(\( 1 - 16 T + 193 T^{2} - 1408 T^{3} + 8299 T^{4} - 29584 T^{5} + 79507 T^{6} \))
$47$ (\( 1 + T + 47 T^{2} \))(\( 1 - 5 T + 47 T^{2} \))(\( 1 + 10 T + 47 T^{2} \))(\( 1 - 8 T + 47 T^{2} \))(\( 1 - 3 T + 47 T^{2} \))(\( 1 - 3 T + 47 T^{2} \))(\( 1 + 8 T + 157 T^{2} + 756 T^{3} + 7379 T^{4} + 17672 T^{5} + 103823 T^{6} \))
$53$ (\( 1 - 6 T + 53 T^{2} \))(\( 1 + 5 T + 53 T^{2} \))(\( 1 + 2 T + 53 T^{2} \))(\( 1 - 6 T + 53 T^{2} \))(\( 1 + 5 T + 53 T^{2} \))(\( 1 - 2 T + 53 T^{2} \))(\( 1 - 2 T + 155 T^{2} - 208 T^{3} + 8215 T^{4} - 5618 T^{5} + 148877 T^{6} \))
$59$ (\( 1 + 59 T^{2} \))(\( 1 + 12 T + 59 T^{2} \))(\( 1 - 3 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 - 4 T + 59 T^{2} \))(\( 1 + 8 T + 59 T^{2} \))(\( 1 + 15 T + 182 T^{2} + 1459 T^{3} + 10738 T^{4} + 52215 T^{5} + 205379 T^{6} \))
$61$ (\( 1 - 10 T + 61 T^{2} \))(\( 1 - 14 T + 61 T^{2} \))(\( 1 - 5 T + 61 T^{2} \))(\( 1 + 2 T + 61 T^{2} \))(\( 1 - 2 T + 61 T^{2} \))(\( 1 + 10 T + 61 T^{2} \))(\( 1 - T + 86 T^{2} - 285 T^{3} + 5246 T^{4} - 3721 T^{5} + 226981 T^{6} \))
$67$ (\( 1 - 8 T + 67 T^{2} \))(\( 1 + 67 T^{2} \))(\( 1 + 6 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( 1 - 12 T + 67 T^{2} \))(\( 1 - 8 T + 67 T^{2} \))(\( 1 + 12 T + 201 T^{2} + 1460 T^{3} + 13467 T^{4} + 53868 T^{5} + 300763 T^{6} \))
$71$ (\( 1 - 12 T + 71 T^{2} \))(\( 1 + 3 T + 71 T^{2} \))(\( 1 + 6 T + 71 T^{2} \))(\( 1 + 71 T^{2} \))(\( 1 - 9 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 - 18 T + 281 T^{2} - 2456 T^{3} + 19951 T^{4} - 90738 T^{5} + 357911 T^{6} \))
$73$ (\( 1 + 10 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 + 11 T + 73 T^{2} \))(\( 1 - 14 T + 73 T^{2} \))(\( 1 + 14 T + 73 T^{2} \))(\( 1 + 2 T + 73 T^{2} \))(\( 1 + 15 T + 224 T^{2} + 1879 T^{3} + 16352 T^{4} + 79935 T^{5} + 389017 T^{6} \))
$79$ (\( 1 - 9 T + 79 T^{2} \))(\( 1 + 12 T + 79 T^{2} \))(\( 1 - 3 T + 79 T^{2} \))(\( 1 + 79 T^{2} \))(\( 1 - 12 T + 79 T^{2} \))(\( 1 - 9 T + 79 T^{2} \))(\( 1 - 5 T + 180 T^{2} - 551 T^{3} + 14220 T^{4} - 31205 T^{5} + 493039 T^{6} \))
$83$ (\( 1 - 4 T + 83 T^{2} \))(\( 1 + 2 T + 83 T^{2} \))(\( 1 - 7 T + 83 T^{2} \))(\( 1 - 16 T + 83 T^{2} \))(\( 1 - 6 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 + 7 T + 260 T^{2} + 1163 T^{3} + 21580 T^{4} + 48223 T^{5} + 571787 T^{6} \))
$89$ (\( 1 - 12 T + 89 T^{2} \))(\( 1 + 5 T + 89 T^{2} \))(\( 1 - 10 T + 89 T^{2} \))(\( 1 + 6 T + 89 T^{2} \))(\( 1 - 9 T + 89 T^{2} \))(\( 1 - 12 T + 89 T^{2} \))(\( 1 + 6 T - T^{2} - 172 T^{3} - 89 T^{4} + 47526 T^{5} + 704969 T^{6} \))
$97$ (\( 1 - 11 T + 97 T^{2} \))(\( 1 + 2 T + 97 T^{2} \))(\( 1 + 8 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))(\( 1 + 10 T + 97 T^{2} \))(\( 1 - 7 T + 97 T^{2} \))(\( 1 + 24 T + 419 T^{2} + 4528 T^{3} + 40643 T^{4} + 225816 T^{5} + 912673 T^{6} \))
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