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Properties

Label 30345.2
Level 30345
Weight 2
Dimension 20890116
Nonzero newspaces 144
Sturm bound 127844352

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Defining parameters

Level: \( N \) = \( 30345 = 3 \cdot 5 \cdot 7 \cdot 17^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 144 \)
Sturm bound: \(127844352\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(30345))\).

Total New Old
Modular forms 32037888 20934332 11103556
Cusp forms 31884289 20890116 10994173
Eisenstein series 153599 44216 109383

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(30345))\)

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
30345.2.a \(\chi_{30345}(1, \cdot)\) 30345.2.a.a 1 1
30345.2.a.b 1
30345.2.a.c 1
30345.2.a.d 1
30345.2.a.e 1
30345.2.a.f 1
30345.2.a.g 1
30345.2.a.h 1
30345.2.a.i 1
30345.2.a.j 1
30345.2.a.k 1
30345.2.a.l 1
30345.2.a.m 1
30345.2.a.n 1
30345.2.a.o 1
30345.2.a.p 1
30345.2.a.q 1
30345.2.a.r 1
30345.2.a.s 1
30345.2.a.t 1
30345.2.a.u 1
30345.2.a.v 1
30345.2.a.w 1
30345.2.a.x 1
30345.2.a.y 1
30345.2.a.z 1
30345.2.a.ba 1
30345.2.a.bb 1
30345.2.a.bc 1
30345.2.a.bd 1
30345.2.a.be 1
30345.2.a.bf 1
30345.2.a.bg 1
30345.2.a.bh 1
30345.2.a.bi 1
30345.2.a.bj 1
30345.2.a.bk 2
30345.2.a.bl 2
30345.2.a.bm 2
30345.2.a.bn 2
30345.2.a.bo 2
30345.2.a.bp 2
30345.2.a.bq 2
30345.2.a.br 2
30345.2.a.bs 2
30345.2.a.bt 2
30345.2.a.bu 3
30345.2.a.bv 3
30345.2.a.bw 3
30345.2.a.bx 3
30345.2.a.by 3
30345.2.a.bz 3
30345.2.a.ca 3
30345.2.a.cb 3
30345.2.a.cc 4
30345.2.a.cd 4
30345.2.a.ce 4
30345.2.a.cf 5
30345.2.a.cg 5
30345.2.a.ch 5
30345.2.a.ci 5
30345.2.a.cj 6
30345.2.a.ck 6
30345.2.a.cl 6
30345.2.a.cm 6
30345.2.a.cn 6
30345.2.a.co 6
30345.2.a.cp 6
30345.2.a.cq 6
30345.2.a.cr 6
30345.2.a.cs 6
30345.2.a.ct 6
30345.2.a.cu 7
30345.2.a.cv 7
30345.2.a.cw 7
30345.2.a.cx 7
30345.2.a.cy 8
30345.2.a.cz 8
30345.2.a.da 8
30345.2.a.db 8
30345.2.a.dc 9
30345.2.a.dd 9
30345.2.a.de 9
30345.2.a.df 9
30345.2.a.dg 10
30345.2.a.dh 10
30345.2.a.di 10
30345.2.a.dj 10
30345.2.a.dk 15
30345.2.a.dl 15
30345.2.a.dm 16
30345.2.a.dn 16
30345.2.a.do 16
30345.2.a.dp 16
30345.2.a.dq 18
30345.2.a.dr 18
30345.2.a.ds 20
30345.2.a.dt 20
30345.2.a.du 24
30345.2.a.dv 24
30345.2.a.dw 24
30345.2.a.dx 24
30345.2.a.dy 24
30345.2.a.dz 24
30345.2.a.ea 24
30345.2.a.eb 24
30345.2.a.ec 30
30345.2.a.ed 30
30345.2.a.ee 30
30345.2.a.ef 30
30345.2.a.eg 32
30345.2.a.eh 32
30345.2.a.ei 32
30345.2.a.ej 32
30345.2.a.ek 40
30345.2.a.el 40
30345.2.a.em 40
30345.2.a.en 40
30345.2.b \(\chi_{30345}(15896, \cdot)\) n/a 2892 1
30345.2.c \(\chi_{30345}(14449, \cdot)\) n/a 1616 1
30345.2.f \(\chi_{30345}(18206, \cdot)\) n/a 2880 1
30345.2.g \(\chi_{30345}(12139, \cdot)\) n/a 1624 1
30345.2.l \(\chi_{30345}(28034, \cdot)\) n/a 4276 1
30345.2.m \(\chi_{30345}(2311, \cdot)\) n/a 1080 1
30345.2.p \(\chi_{30345}(30344, \cdot)\) n/a 4264 1
30345.2.q \(\chi_{30345}(17341, \cdot)\) n/a 2892 2
30345.2.t \(\chi_{30345}(14701, \cdot)\) n/a 2160 2
30345.2.u \(\chi_{30345}(12389, \cdot)\) n/a 8528 2
30345.2.v \(\chi_{30345}(8093, \cdot)\) n/a 6504 2
30345.2.x \(\chi_{30345}(16183, \cdot)\) n/a 4320 2
30345.2.z \(\chi_{30345}(1483, \cdot)\) n/a 4320 2
30345.2.bc \(\chi_{30345}(7552, \cdot)\) n/a 4320 2
30345.2.be \(\chi_{30345}(26048, \cdot)\) n/a 6480 2
30345.2.bf \(\chi_{30345}(1772, \cdot)\) n/a 6480 2
30345.2.bh \(\chi_{30345}(10403, \cdot)\) n/a 6480 2
30345.2.bj \(\chi_{30345}(13873, \cdot)\) n/a 4336 2
30345.2.bl \(\chi_{30345}(26839, \cdot)\) n/a 3232 2
30345.2.bm \(\chi_{30345}(251, \cdot)\) n/a 5760 2
30345.2.br \(\chi_{30345}(8669, \cdot)\) n/a 8528 2
30345.2.bu \(\chi_{30345}(19651, \cdot)\) n/a 2880 2
30345.2.bv \(\chi_{30345}(6359, \cdot)\) n/a 8552 2
30345.2.bw \(\chi_{30345}(3469, \cdot)\) n/a 4336 2
30345.2.bx \(\chi_{30345}(866, \cdot)\) n/a 5760 2
30345.2.ca \(\chi_{30345}(1444, \cdot)\) n/a 4320 2
30345.2.cb \(\chi_{30345}(24566, \cdot)\) n/a 5780 2
30345.2.ce \(\chi_{30345}(9358, \cdot)\) n/a 8640 4
30345.2.ch \(\chi_{30345}(6203, \cdot)\) n/a 12960 4
30345.2.cj \(\chi_{30345}(4201, \cdot)\) n/a 4320 4
30345.2.ck \(\chi_{30345}(1889, \cdot)\) n/a 17056 4
30345.2.cn \(\chi_{30345}(11381, \cdot)\) n/a 11520 4
30345.2.co \(\chi_{30345}(7624, \cdot)\) n/a 6496 4
30345.2.cq \(\chi_{30345}(3578, \cdot)\) n/a 12960 4
30345.2.ct \(\chi_{30345}(11983, \cdot)\) n/a 8640 4
30345.2.cu \(\chi_{30345}(8921, \cdot)\) n/a 11520 4
30345.2.cv \(\chi_{30345}(13834, \cdot)\) n/a 8640 4
30345.2.cz \(\chi_{30345}(2602, \cdot)\) n/a 8672 4
30345.2.db \(\chi_{30345}(1733, \cdot)\) n/a 17056 4
30345.2.dc \(\chi_{30345}(13043, \cdot)\) n/a 17056 4
30345.2.df \(\chi_{30345}(9788, \cdot)\) n/a 17056 4
30345.2.dh \(\chi_{30345}(10153, \cdot)\) n/a 8640 4
30345.2.di \(\chi_{30345}(6898, \cdot)\) n/a 8640 4
30345.2.dl \(\chi_{30345}(577, \cdot)\) n/a 8640 4
30345.2.dn \(\chi_{30345}(1157, \cdot)\) n/a 17104 4
30345.2.dq \(\chi_{30345}(21059, \cdot)\) n/a 17056 4
30345.2.dr \(\chi_{30345}(1696, \cdot)\) n/a 5760 4
30345.2.ds \(\chi_{30345}(503, \cdot)\) n/a 34112 8
30345.2.du \(\chi_{30345}(3403, \cdot)\) n/a 12960 8
30345.2.dx \(\chi_{30345}(1231, \cdot)\) n/a 11520 8
30345.2.dy \(\chi_{30345}(2759, \cdot)\) n/a 25920 8
30345.2.ea \(\chi_{30345}(5426, \cdot)\) n/a 17280 8
30345.2.ed \(\chi_{30345}(4549, \cdot)\) n/a 17280 8
30345.2.ee \(\chi_{30345}(3508, \cdot)\) n/a 12960 8
30345.2.eg \(\chi_{30345}(4493, \cdot)\) n/a 34112 8
30345.2.ei \(\chi_{30345}(1786, \cdot)\) n/a 19584 16
30345.2.ej \(\chi_{30345}(1913, \cdot)\) n/a 34112 8
30345.2.em \(\chi_{30345}(733, \cdot)\) n/a 17280 8
30345.2.eo \(\chi_{30345}(1844, \cdot)\) n/a 34112 8
30345.2.ep \(\chi_{30345}(12826, \cdot)\) n/a 11520 8
30345.2.es \(\chi_{30345}(1579, \cdot)\) n/a 17280 8
30345.2.et \(\chi_{30345}(1046, \cdot)\) n/a 23040 8
30345.2.ev \(\chi_{30345}(712, \cdot)\) n/a 17280 8
30345.2.ey \(\chi_{30345}(977, \cdot)\) n/a 34112 8
30345.2.ez \(\chi_{30345}(1784, \cdot)\) n/a 78208 16
30345.2.fc \(\chi_{30345}(526, \cdot)\) n/a 19584 16
30345.2.fd \(\chi_{30345}(1259, \cdot)\) n/a 78208 16
30345.2.fi \(\chi_{30345}(1429, \cdot)\) n/a 29440 16
30345.2.fj \(\chi_{30345}(356, \cdot)\) n/a 52224 16
30345.2.fm \(\chi_{30345}(169, \cdot)\) n/a 29440 16
30345.2.fn \(\chi_{30345}(1616, \cdot)\) n/a 52224 16
30345.2.fp \(\chi_{30345}(907, \cdot)\) n/a 34560 16
30345.2.fr \(\chi_{30345}(2063, \cdot)\) n/a 68224 16
30345.2.fs \(\chi_{30345}(1669, \cdot)\) n/a 34560 16
30345.2.fv \(\chi_{30345}(3971, \cdot)\) n/a 46080 16
30345.2.fx \(\chi_{30345}(4559, \cdot)\) n/a 68224 16
30345.2.fy \(\chi_{30345}(1081, \cdot)\) n/a 23040 16
30345.2.gb \(\chi_{30345}(1958, \cdot)\) n/a 68224 16
30345.2.gd \(\chi_{30345}(802, \cdot)\) n/a 34560 16
30345.2.ge \(\chi_{30345}(256, \cdot)\) n/a 52224 32
30345.2.gh \(\chi_{30345}(1721, \cdot)\) n/a 104448 32
30345.2.gi \(\chi_{30345}(64, \cdot)\) n/a 58880 32
30345.2.gk \(\chi_{30345}(307, \cdot)\) n/a 78336 32
30345.2.gm \(\chi_{30345}(407, \cdot)\) n/a 117504 32
30345.2.go \(\chi_{30345}(1373, \cdot)\) n/a 117504 32
30345.2.gp \(\chi_{30345}(302, \cdot)\) n/a 117504 32
30345.2.gr \(\chi_{30345}(13, \cdot)\) n/a 78336 32
30345.2.gu \(\chi_{30345}(727, \cdot)\) n/a 78336 32
30345.2.gw \(\chi_{30345}(118, \cdot)\) n/a 78336 32
30345.2.gy \(\chi_{30345}(953, \cdot)\) n/a 117504 32
30345.2.gz \(\chi_{30345}(1364, \cdot)\) n/a 156416 32
30345.2.ha \(\chi_{30345}(106, \cdot)\) n/a 39168 32
30345.2.hf \(\chi_{30345}(341, \cdot)\) n/a 104448 32
30345.2.hg \(\chi_{30345}(424, \cdot)\) n/a 78336 32
30345.2.hj \(\chi_{30345}(101, \cdot)\) n/a 104448 32
30345.2.hk \(\chi_{30345}(919, \cdot)\) n/a 78336 32
30345.2.hl \(\chi_{30345}(1004, \cdot)\) n/a 156416 32
30345.2.hm \(\chi_{30345}(16, \cdot)\) n/a 52224 32
30345.2.hp \(\chi_{30345}(509, \cdot)\) n/a 156416 32
30345.2.hs \(\chi_{30345}(223, \cdot)\) n/a 156672 64
30345.2.hv \(\chi_{30345}(8, \cdot)\) n/a 235008 64
30345.2.hw \(\chi_{30345}(461, \cdot)\) n/a 208896 64
30345.2.hz \(\chi_{30345}(274, \cdot)\) n/a 117248 64
30345.2.ia \(\chi_{30345}(631, \cdot)\) n/a 78336 64
30345.2.id \(\chi_{30345}(104, \cdot)\) n/a 312832 64
30345.2.ie \(\chi_{30345}(722, \cdot)\) n/a 235008 64
30345.2.ih \(\chi_{30345}(202, \cdot)\) n/a 156672 64
30345.2.ii \(\chi_{30345}(361, \cdot)\) n/a 104448 64
30345.2.ij \(\chi_{30345}(89, \cdot)\) n/a 312832 64
30345.2.im \(\chi_{30345}(137, \cdot)\) n/a 312832 64
30345.2.io \(\chi_{30345}(628, \cdot)\) n/a 156672 64
30345.2.ir \(\chi_{30345}(157, \cdot)\) n/a 156672 64
30345.2.is \(\chi_{30345}(208, \cdot)\) n/a 156672 64
30345.2.iu \(\chi_{30345}(242, \cdot)\) n/a 312832 64
30345.2.ix \(\chi_{30345}(548, \cdot)\) n/a 312832 64
30345.2.iy \(\chi_{30345}(662, \cdot)\) n/a 312832 64
30345.2.ja \(\chi_{30345}(52, \cdot)\) n/a 156672 64
30345.2.je \(\chi_{30345}(4, \cdot)\) n/a 156672 64
30345.2.jf \(\chi_{30345}(446, \cdot)\) n/a 208896 64
30345.2.jh \(\chi_{30345}(22, \cdot)\) n/a 235008 128
30345.2.jj \(\chi_{30345}(62, \cdot)\) n/a 625664 128
30345.2.jk \(\chi_{30345}(139, \cdot)\) n/a 313344 128
30345.2.jn \(\chi_{30345}(71, \cdot)\) n/a 313344 128
30345.2.jp \(\chi_{30345}(29, \cdot)\) n/a 470016 128
30345.2.jq \(\chi_{30345}(181, \cdot)\) n/a 208896 128
30345.2.jt \(\chi_{30345}(167, \cdot)\) n/a 625664 128
30345.2.jv \(\chi_{30345}(148, \cdot)\) n/a 235008 128
30345.2.jw \(\chi_{30345}(53, \cdot)\) n/a 625664 128
30345.2.jz \(\chi_{30345}(178, \cdot)\) n/a 313344 128
30345.2.ka \(\chi_{30345}(529, \cdot)\) n/a 313344 128
30345.2.kd \(\chi_{30345}(26, \cdot)\) n/a 417792 128
30345.2.ke \(\chi_{30345}(59, \cdot)\) n/a 625664 128
30345.2.kh \(\chi_{30345}(121, \cdot)\) n/a 208896 128
30345.2.ki \(\chi_{30345}(502, \cdot)\) n/a 313344 128
30345.2.kl \(\chi_{30345}(2, \cdot)\) n/a 625664 128
30345.2.km \(\chi_{30345}(173, \cdot)\) n/a 1251328 256
30345.2.ko \(\chi_{30345}(37, \cdot)\) n/a 626688 256
30345.2.kr \(\chi_{30345}(31, \cdot)\) n/a 417792 256
30345.2.ks \(\chi_{30345}(44, \cdot)\) n/a 1251328 256
30345.2.ku \(\chi_{30345}(11, \cdot)\) n/a 835584 256
30345.2.kx \(\chi_{30345}(124, \cdot)\) n/a 626688 256
30345.2.ky \(\chi_{30345}(88, \cdot)\) n/a 626688 256
30345.2.la \(\chi_{30345}(122, \cdot)\) n/a 1251328 256

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(30345))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(30345)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(255))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(289))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(357))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(595))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(867))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1445))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1785))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2023))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4335))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6069))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10115))\)\(^{\oplus 2}\)