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Properties

Label 15210.2
Level 15210
Weight 2
Dimension 1465979
Nonzero newspaces 100
Sturm bound 24530688

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Defining parameters

Level: \( N \) = \( 15210 = 2 \cdot 3^{2} \cdot 5 \cdot 13^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 100 \)
Sturm bound: \(24530688\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(15210))\).

Total New Old
Modular forms 6161856 1465979 4695877
Cusp forms 6103489 1465979 4637510
Eisenstein series 58367 0 58367

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(15210))\)

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
15210.2.a \(\chi_{15210}(1, \cdot)\) 15210.2.a.a 1 1
15210.2.a.b 1
15210.2.a.c 1
15210.2.a.d 1
15210.2.a.e 1
15210.2.a.f 1
15210.2.a.g 1
15210.2.a.h 1
15210.2.a.i 1
15210.2.a.j 1
15210.2.a.k 1
15210.2.a.l 1
15210.2.a.m 1
15210.2.a.n 1
15210.2.a.o 1
15210.2.a.p 1
15210.2.a.q 1
15210.2.a.r 1
15210.2.a.s 1
15210.2.a.t 1
15210.2.a.u 1
15210.2.a.v 1
15210.2.a.w 1
15210.2.a.x 1
15210.2.a.y 1
15210.2.a.z 1
15210.2.a.ba 1
15210.2.a.bb 1
15210.2.a.bc 1
15210.2.a.bd 1
15210.2.a.be 1
15210.2.a.bf 1
15210.2.a.bg 1
15210.2.a.bh 1
15210.2.a.bi 1
15210.2.a.bj 1
15210.2.a.bk 1
15210.2.a.bl 1
15210.2.a.bm 1
15210.2.a.bn 1
15210.2.a.bo 1
15210.2.a.bp 1
15210.2.a.bq 1
15210.2.a.br 1
15210.2.a.bs 1
15210.2.a.bt 1
15210.2.a.bu 1
15210.2.a.bv 2
15210.2.a.bw 2
15210.2.a.bx 2
15210.2.a.by 2
15210.2.a.bz 2
15210.2.a.ca 2
15210.2.a.cb 2
15210.2.a.cc 2
15210.2.a.cd 2
15210.2.a.ce 2
15210.2.a.cf 2
15210.2.a.cg 2
15210.2.a.ch 2
15210.2.a.ci 2
15210.2.a.cj 2
15210.2.a.ck 2
15210.2.a.cl 2
15210.2.a.cm 2
15210.2.a.cn 2
15210.2.a.co 2
15210.2.a.cp 2
15210.2.a.cq 2
15210.2.a.cr 2
15210.2.a.cs 2
15210.2.a.ct 2
15210.2.a.cu 2
15210.2.a.cv 2
15210.2.a.cw 2
15210.2.a.cx 2
15210.2.a.cy 3
15210.2.a.cz 3
15210.2.a.da 3
15210.2.a.db 3
15210.2.a.dc 3
15210.2.a.dd 3
15210.2.a.de 3
15210.2.a.df 3
15210.2.a.dg 3
15210.2.a.dh 3
15210.2.a.di 3
15210.2.a.dj 3
15210.2.a.dk 3
15210.2.a.dl 3
15210.2.a.dm 3
15210.2.a.dn 3
15210.2.a.do 3
15210.2.a.dp 3
15210.2.a.dq 3
15210.2.a.dr 3
15210.2.a.ds 4
15210.2.a.dt 4
15210.2.a.du 4
15210.2.a.dv 4
15210.2.a.dw 4
15210.2.a.dx 4
15210.2.a.dy 4
15210.2.a.dz 4
15210.2.a.ea 6
15210.2.a.eb 6
15210.2.a.ec 6
15210.2.a.ed 6
15210.2.a.ee 6
15210.2.a.ef 6
15210.2.a.eg 6
15210.2.a.eh 6
15210.2.a.ei 6
15210.2.a.ej 6
15210.2.b \(\chi_{15210}(1351, \cdot)\) n/a 254 1
15210.2.e \(\chi_{15210}(12169, \cdot)\) n/a 388 1
15210.2.f \(\chi_{15210}(13519, \cdot)\) n/a 384 1
15210.2.i \(\chi_{15210}(991, \cdot)\) n/a 516 2
15210.2.j \(\chi_{15210}(5071, \cdot)\) n/a 1240 2
15210.2.k \(\chi_{15210}(11131, \cdot)\) n/a 1232 2
15210.2.l \(\chi_{15210}(3571, \cdot)\) n/a 1232 2
15210.2.m \(\chi_{15210}(577, \cdot)\) n/a 770 2
15210.2.o \(\chi_{15210}(4733, \cdot)\) n/a 620 2
15210.2.q \(\chi_{15210}(5309, \cdot)\) n/a 616 2
15210.2.s \(\chi_{15210}(8351, \cdot)\) n/a 400 2
15210.2.v \(\chi_{15210}(6083, \cdot)\) n/a 616 2
15210.2.w \(\chi_{15210}(3817, \cdot)\) n/a 770 2
15210.2.y \(\chi_{15210}(529, \cdot)\) n/a 1848 2
15210.2.bb \(\chi_{15210}(2851, \cdot)\) n/a 1232 2
15210.2.bd \(\chi_{15210}(7459, \cdot)\) n/a 1848 2
15210.2.bg \(\chi_{15210}(3379, \cdot)\) n/a 1848 2
15210.2.bj \(\chi_{15210}(4879, \cdot)\) n/a 768 2
15210.2.bm \(\chi_{15210}(10501, \cdot)\) n/a 1232 2
15210.2.bo \(\chi_{15210}(2029, \cdot)\) n/a 1860 2
15210.2.bp \(\chi_{15210}(5599, \cdot)\) n/a 772 2
15210.2.bs \(\chi_{15210}(361, \cdot)\) n/a 516 2
15210.2.bt \(\chi_{15210}(6421, \cdot)\) n/a 1232 2
15210.2.bv \(\chi_{15210}(8089, \cdot)\) n/a 1848 2
15210.2.bz \(\chi_{15210}(2389, \cdot)\) n/a 1848 2
15210.2.cb \(\chi_{15210}(7117, \cdot)\) n/a 3696 4
15210.2.cc \(\chi_{15210}(5497, \cdot)\) n/a 3696 4
15210.2.cf \(\chi_{15210}(2953, \cdot)\) n/a 1540 4
15210.2.cg \(\chi_{15210}(4633, \cdot)\) n/a 3696 4
15210.2.cj \(\chi_{15210}(1667, \cdot)\) n/a 3696 4
15210.2.cl \(\chi_{15210}(3527, \cdot)\) n/a 1232 4
15210.2.cm \(\chi_{15210}(23, \cdot)\) n/a 3696 4
15210.2.cp \(\chi_{15210}(1013, \cdot)\) n/a 3696 4
15210.2.cr \(\chi_{15210}(239, \cdot)\) n/a 3696 4
15210.2.cs \(\chi_{15210}(6671, \cdot)\) n/a 2464 4
15210.2.cu \(\chi_{15210}(1601, \cdot)\) n/a 832 4
15210.2.cx \(\chi_{15210}(5051, \cdot)\) n/a 2464 4
15210.2.cz \(\chi_{15210}(2009, \cdot)\) n/a 3696 4
15210.2.da \(\chi_{15210}(3629, \cdot)\) n/a 3696 4
15210.2.dc \(\chi_{15210}(89, \cdot)\) n/a 1232 4
15210.2.df \(\chi_{15210}(1451, \cdot)\) n/a 2464 4
15210.2.dg \(\chi_{15210}(677, \cdot)\) n/a 3720 4
15210.2.dj \(\chi_{15210}(653, \cdot)\) n/a 3696 4
15210.2.dk \(\chi_{15210}(4247, \cdot)\) n/a 1232 4
15210.2.dm \(\chi_{15210}(1037, \cdot)\) n/a 3696 4
15210.2.do \(\chi_{15210}(2047, \cdot)\) n/a 3696 4
15210.2.dr \(\chi_{15210}(2803, \cdot)\) n/a 3696 4
15210.2.ds \(\chi_{15210}(1333, \cdot)\) n/a 1540 4
15210.2.dv \(\chi_{15210}(427, \cdot)\) n/a 3696 4
15210.2.dw \(\chi_{15210}(1171, \cdot)\) n/a 3672 12
15210.2.dy \(\chi_{15210}(649, \cdot)\) n/a 5472 12
15210.2.eb \(\chi_{15210}(469, \cdot)\) n/a 5448 12
15210.2.ec \(\chi_{15210}(181, \cdot)\) n/a 3672 12
15210.2.ee \(\chi_{15210}(61, \cdot)\) n/a 17472 24
15210.2.ef \(\chi_{15210}(601, \cdot)\) n/a 17472 24
15210.2.eg \(\chi_{15210}(391, \cdot)\) n/a 17472 24
15210.2.eh \(\chi_{15210}(451, \cdot)\) n/a 7248 24
15210.2.ej \(\chi_{15210}(307, \cdot)\) n/a 10920 24
15210.2.el \(\chi_{15210}(233, \cdot)\) n/a 8736 24
15210.2.en \(\chi_{15210}(161, \cdot)\) n/a 5952 24
15210.2.ep \(\chi_{15210}(359, \cdot)\) n/a 8736 24
15210.2.eq \(\chi_{15210}(53, \cdot)\) n/a 8736 24
15210.2.et \(\chi_{15210}(73, \cdot)\) n/a 10920 24
15210.2.ev \(\chi_{15210}(49, \cdot)\) n/a 26208 24
15210.2.ex \(\chi_{15210}(139, \cdot)\) n/a 26208 24
15210.2.ez \(\chi_{15210}(571, \cdot)\) n/a 17472 24
15210.2.fc \(\chi_{15210}(901, \cdot)\) n/a 7248 24
15210.2.fd \(\chi_{15210}(289, \cdot)\) n/a 10896 24
15210.2.fg \(\chi_{15210}(79, \cdot)\) n/a 26208 24
15210.2.fi \(\chi_{15210}(121, \cdot)\) n/a 17472 24
15210.2.fl \(\chi_{15210}(199, \cdot)\) n/a 10944 24
15210.2.fm \(\chi_{15210}(259, \cdot)\) n/a 26208 24
15210.2.fr \(\chi_{15210}(439, \cdot)\) n/a 26208 24
15210.2.ft \(\chi_{15210}(511, \cdot)\) n/a 17472 24
15210.2.fu \(\chi_{15210}(679, \cdot)\) n/a 26208 24
15210.2.fw \(\chi_{15210}(7, \cdot)\) n/a 52416 48
15210.2.fz \(\chi_{15210}(163, \cdot)\) n/a 21840 48
15210.2.ga \(\chi_{15210}(187, \cdot)\) n/a 52416 48
15210.2.gd \(\chi_{15210}(457, \cdot)\) n/a 52416 48
15210.2.ge \(\chi_{15210}(563, \cdot)\) n/a 52416 48
15210.2.gg \(\chi_{15210}(443, \cdot)\) n/a 52416 48
15210.2.gj \(\chi_{15210}(107, \cdot)\) n/a 17472 48
15210.2.gk \(\chi_{15210}(887, \cdot)\) n/a 52416 48
15210.2.gm \(\chi_{15210}(281, \cdot)\) n/a 34944 48
15210.2.go \(\chi_{15210}(509, \cdot)\) n/a 52416 48
15210.2.gr \(\chi_{15210}(449, \cdot)\) n/a 17472 48
15210.2.gt \(\chi_{15210}(59, \cdot)\) n/a 52416 48
15210.2.gv \(\chi_{15210}(71, \cdot)\) n/a 11520 48
15210.2.gx \(\chi_{15210}(11, \cdot)\) n/a 34944 48
15210.2.gy \(\chi_{15210}(41, \cdot)\) n/a 34944 48
15210.2.ha \(\chi_{15210}(749, \cdot)\) n/a 52416 48
15210.2.hd \(\chi_{15210}(173, \cdot)\) n/a 52416 48
15210.2.he \(\chi_{15210}(17, \cdot)\) n/a 17472 48
15210.2.hh \(\chi_{15210}(77, \cdot)\) n/a 52416 48
15210.2.hj \(\chi_{15210}(113, \cdot)\) n/a 52416 48
15210.2.hl \(\chi_{15210}(697, \cdot)\) n/a 52416 48
15210.2.hm \(\chi_{15210}(37, \cdot)\) n/a 21840 48
15210.2.hp \(\chi_{15210}(223, \cdot)\) n/a 52416 48
15210.2.hq \(\chi_{15210}(67, \cdot)\) n/a 52416 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(15210))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(15210)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(130))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(195))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(234))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(390))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(507))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(585))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(845))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1014))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1170))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1521))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1690))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2535))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3042))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5070))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7605))\)\(^{\oplus 2}\)