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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 available 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

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