↑

Properties

Label 9310.2
Level 9310
Weight 2
Dimension 740676
Nonzero newspaces 96
Sturm bound 10160640

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 9310 = 2 \cdot 5 \cdot 7^{2} \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 96 \)
Sturm bound: \(10160640\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9310))\).

Total New Old
Modular forms 2557440 740676 1816764
Cusp forms 2522881 740676 1782205
Eisenstein series 34559 0 34559

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9310))\)

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
9310.2.a \(\chi_{9310}(1, \cdot)\) 9310.2.a.a 1 1
9310.2.a.b 1
9310.2.a.c 1
9310.2.a.d 1
9310.2.a.e 1
9310.2.a.f 1
9310.2.a.g 1
9310.2.a.h 1
9310.2.a.i 1
9310.2.a.j 1
9310.2.a.k 1
9310.2.a.l 1
9310.2.a.m 1
9310.2.a.n 1
9310.2.a.o 1
9310.2.a.p 1
9310.2.a.q 1
9310.2.a.r 1
9310.2.a.s 1
9310.2.a.t 1
9310.2.a.u 1
9310.2.a.v 2
9310.2.a.w 2
9310.2.a.x 2
9310.2.a.y 2
9310.2.a.z 2
9310.2.a.ba 2
9310.2.a.bb 2
9310.2.a.bc 2
9310.2.a.bd 2
9310.2.a.be 2
9310.2.a.bf 2
9310.2.a.bg 3
9310.2.a.bh 3
9310.2.a.bi 3
9310.2.a.bj 3
9310.2.a.bk 3
9310.2.a.bl 3
9310.2.a.bm 3
9310.2.a.bn 4
9310.2.a.bo 4
9310.2.a.bp 4
9310.2.a.bq 4
9310.2.a.br 4
9310.2.a.bs 4
9310.2.a.bt 4
9310.2.a.bu 4
9310.2.a.bv 4
9310.2.a.bw 4
9310.2.a.bx 5
9310.2.a.by 5
9310.2.a.bz 5
9310.2.a.ca 5
9310.2.a.cb 5
9310.2.a.cc 5
9310.2.a.cd 6
9310.2.a.ce 6
9310.2.a.cf 7
9310.2.a.cg 7
9310.2.a.ch 7
9310.2.a.ci 7
9310.2.a.cj 8
9310.2.a.ck 8
9310.2.a.cl 8
9310.2.a.cm 8
9310.2.a.cn 10
9310.2.a.co 10
9310.2.a.cp 10
9310.2.a.cq 10
9310.2.b \(\chi_{9310}(7449, \cdot)\) n/a 370 1
9310.2.d \(\chi_{9310}(9309, \cdot)\) n/a 400 1
9310.2.g \(\chi_{9310}(1861, \cdot)\) n/a 272 1
9310.2.i \(\chi_{9310}(1341, \cdot)\) n/a 528 2
9310.2.j \(\chi_{9310}(6841, \cdot)\) n/a 480 2
9310.2.k \(\chi_{9310}(3431, \cdot)\) n/a 552 2
9310.2.l \(\chi_{9310}(961, \cdot)\) n/a 528 2
9310.2.m \(\chi_{9310}(2547, \cdot)\) n/a 720 2
9310.2.o \(\chi_{9310}(1177, \cdot)\) n/a 820 2
9310.2.q \(\chi_{9310}(8409, \cdot)\) n/a 800 2
9310.2.s \(\chi_{9310}(7479, \cdot)\) n/a 800 2
9310.2.v \(\chi_{9310}(411, \cdot)\) n/a 528 2
9310.2.y \(\chi_{9310}(3951, \cdot)\) n/a 528 2
9310.2.bb \(\chi_{9310}(7251, \cdot)\) n/a 544 2
9310.2.be \(\chi_{9310}(2089, \cdot)\) n/a 800 2
9310.2.bg \(\chi_{9310}(4979, \cdot)\) n/a 720 2
9310.2.bi \(\chi_{9310}(7859, \cdot)\) n/a 800 2
9310.2.bk \(\chi_{9310}(8789, \cdot)\) n/a 800 2
9310.2.bm \(\chi_{9310}(5389, \cdot)\) n/a 800 2
9310.2.bo \(\chi_{9310}(1569, \cdot)\) n/a 820 2
9310.2.bq \(\chi_{9310}(31, \cdot)\) n/a 528 2
9310.2.bs \(\chi_{9310}(1331, \cdot)\) n/a 2016 6
9310.2.bt \(\chi_{9310}(491, \cdot)\) n/a 1632 6
9310.2.bu \(\chi_{9310}(3901, \cdot)\) n/a 1608 6
9310.2.bv \(\chi_{9310}(4281, \cdot)\) n/a 1608 6
9310.2.bx \(\chi_{9310}(753, \cdot)\) n/a 1600 4
9310.2.bz \(\chi_{9310}(4723, \cdot)\) n/a 1600 4
9310.2.cb \(\chi_{9310}(913, \cdot)\) n/a 1440 4
9310.2.cd \(\chi_{9310}(373, \cdot)\) n/a 1600 4
9310.2.cf \(\chi_{9310}(4343, \cdot)\) n/a 1600 4
9310.2.ch \(\chi_{9310}(4293, \cdot)\) n/a 1600 4
9310.2.ci \(\chi_{9310}(2843, \cdot)\) n/a 1640 4
9310.2.ck \(\chi_{9310}(2253, \cdot)\) n/a 1600 4
9310.2.cn \(\chi_{9310}(531, \cdot)\) n/a 2208 6
9310.2.cq \(\chi_{9310}(1329, \cdot)\) n/a 3360 6
9310.2.cs \(\chi_{9310}(799, \cdot)\) n/a 3024 6
9310.2.cv \(\chi_{9310}(1371, \cdot)\) n/a 1584 6
9310.2.cy \(\chi_{9310}(2371, \cdot)\) n/a 1608 6
9310.2.db \(\chi_{9310}(99, \cdot)\) n/a 2460 6
9310.2.dc \(\chi_{9310}(489, \cdot)\) n/a 2400 6
9310.2.df \(\chi_{9310}(509, \cdot)\) n/a 2400 6
9310.2.dg \(\chi_{9310}(2039, \cdot)\) n/a 2400 6
9310.2.dh \(\chi_{9310}(1991, \cdot)\) n/a 1608 6
9310.2.dk \(\chi_{9310}(129, \cdot)\) n/a 2400 6
9310.2.dl \(\chi_{9310}(2419, \cdot)\) n/a 2400 6
9310.2.do \(\chi_{9310}(501, \cdot)\) n/a 4512 12
9310.2.dp \(\chi_{9310}(771, \cdot)\) n/a 4416 12
9310.2.dq \(\chi_{9310}(191, \cdot)\) n/a 4032 12
9310.2.dr \(\chi_{9310}(11, \cdot)\) n/a 4512 12
9310.2.ds \(\chi_{9310}(113, \cdot)\) n/a 6720 12
9310.2.du \(\chi_{9310}(153, \cdot)\) n/a 6048 12
9310.2.dw \(\chi_{9310}(313, \cdot)\) n/a 4800 12
9310.2.dx \(\chi_{9310}(1047, \cdot)\) n/a 4800 12
9310.2.ea \(\chi_{9310}(587, \cdot)\) n/a 4800 12
9310.2.eb \(\chi_{9310}(393, \cdot)\) n/a 4920 12
9310.2.eg \(\chi_{9310}(803, \cdot)\) n/a 4800 12
9310.2.eh \(\chi_{9310}(67, \cdot)\) n/a 4800 12
9310.2.ej \(\chi_{9310}(1361, \cdot)\) n/a 4512 12
9310.2.el \(\chi_{9310}(239, \cdot)\) n/a 6720 12
9310.2.en \(\chi_{9310}(69, \cdot)\) n/a 6720 12
9310.2.ep \(\chi_{9310}(809, \cdot)\) n/a 6720 12
9310.2.er \(\chi_{9310}(1209, \cdot)\) n/a 6720 12
9310.2.et \(\chi_{9310}(39, \cdot)\) n/a 6048 12
9310.2.ev \(\chi_{9310}(759, \cdot)\) n/a 6720 12
9310.2.ey \(\chi_{9310}(601, \cdot)\) n/a 4416 12
9310.2.fb \(\chi_{9310}(341, \cdot)\) n/a 4512 12
9310.2.fe \(\chi_{9310}(1741, \cdot)\) n/a 4512 12
9310.2.fh \(\chi_{9310}(369, \cdot)\) n/a 6720 12
9310.2.fj \(\chi_{9310}(429, \cdot)\) n/a 6720 12
9310.2.fk \(\chi_{9310}(291, \cdot)\) n/a 13392 36
9310.2.fl \(\chi_{9310}(351, \cdot)\) n/a 13536 36
9310.2.fm \(\chi_{9310}(81, \cdot)\) n/a 13392 36
9310.2.fn \(\chi_{9310}(83, \cdot)\) n/a 13440 24
9310.2.fp \(\chi_{9310}(183, \cdot)\) n/a 13440 24
9310.2.fs \(\chi_{9310}(37, \cdot)\) n/a 13440 24
9310.2.fu \(\chi_{9310}(87, \cdot)\) n/a 13440 24
9310.2.fw \(\chi_{9310}(107, \cdot)\) n/a 13440 24
9310.2.fy \(\chi_{9310}(647, \cdot)\) n/a 12096 24
9310.2.ga \(\chi_{9310}(467, \cdot)\) n/a 13440 24
9310.2.gc \(\chi_{9310}(487, \cdot)\) n/a 13440 24
9310.2.gd \(\chi_{9310}(149, \cdot)\) n/a 20160 36
9310.2.ge \(\chi_{9310}(299, \cdot)\) n/a 20160 36
9310.2.gh \(\chi_{9310}(241, \cdot)\) n/a 13392 36
9310.2.gm \(\chi_{9310}(279, \cdot)\) n/a 20160 36
9310.2.gn \(\chi_{9310}(169, \cdot)\) n/a 20160 36
9310.2.gq \(\chi_{9310}(9, \cdot)\) n/a 20160 36
9310.2.gr \(\chi_{9310}(59, \cdot)\) n/a 20160 36
9310.2.gu \(\chi_{9310}(41, \cdot)\) n/a 13536 36
9310.2.gx \(\chi_{9310}(451, \cdot)\) n/a 13392 36
9310.2.ha \(\chi_{9310}(53, \cdot)\) n/a 40320 72
9310.2.hb \(\chi_{9310}(187, \cdot)\) n/a 40320 72
9310.2.hc \(\chi_{9310}(193, \cdot)\) n/a 40320 72
9310.2.hd \(\chi_{9310}(17, \cdot)\) n/a 40320 72
9310.2.hg \(\chi_{9310}(127, \cdot)\) n/a 40320 72
9310.2.hh \(\chi_{9310}(237, \cdot)\) n/a 40320 72

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(9310))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(9310)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(133))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(190))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(266))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(490))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(665))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(931))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1330))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1862))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4655))\)\(^{\oplus 2}\)