Properties

 Label 8015.2 Level 8015 Weight 2 Dimension 2.20433e+06 Nonzero newspaces 100 Sturm bound 1.00685e+07

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

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