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Properties

Label 7120.2
Level 7120
Weight 2
Dimension 781532
Nonzero newspaces 76
Sturm bound 6082560

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Defining parameters

Level: \( N \) = \( 7120 = 2^{4} \cdot 5 \cdot 89 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 76 \)
Sturm bound: \(6082560\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7120))\).

Total New Old
Modular forms 1530496 786232 744264
Cusp forms 1510785 781532 729253
Eisenstein series 19711 4700 15011

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7120))\)

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
7120.2.a \(\chi_{7120}(1, \cdot)\) 7120.2.a.a 1 1
7120.2.a.b 1
7120.2.a.c 1
7120.2.a.d 1
7120.2.a.e 1
7120.2.a.f 1
7120.2.a.g 1
7120.2.a.h 1
7120.2.a.i 1
7120.2.a.j 1
7120.2.a.k 1
7120.2.a.l 1
7120.2.a.m 1
7120.2.a.n 1
7120.2.a.o 1
7120.2.a.p 1
7120.2.a.q 1
7120.2.a.r 2
7120.2.a.s 2
7120.2.a.t 2
7120.2.a.u 2
7120.2.a.v 2
7120.2.a.w 2
7120.2.a.x 3
7120.2.a.y 3
7120.2.a.z 4
7120.2.a.ba 4
7120.2.a.bb 4
7120.2.a.bc 4
7120.2.a.bd 5
7120.2.a.be 5
7120.2.a.bf 6
7120.2.a.bg 6
7120.2.a.bh 6
7120.2.a.bi 6
7120.2.a.bj 7
7120.2.a.bk 8
7120.2.a.bl 8
7120.2.a.bm 9
7120.2.a.bn 10
7120.2.a.bo 11
7120.2.a.bp 12
7120.2.a.bq 12
7120.2.a.br 14
7120.2.d \(\chi_{7120}(2849, \cdot)\) n/a 264 1
7120.2.e \(\chi_{7120}(1601, \cdot)\) n/a 180 1
7120.2.f \(\chi_{7120}(889, \cdot)\) None 0 1
7120.2.g \(\chi_{7120}(3561, \cdot)\) None 0 1
7120.2.j \(\chi_{7120}(6409, \cdot)\) None 0 1
7120.2.k \(\chi_{7120}(5161, \cdot)\) None 0 1
7120.2.p \(\chi_{7120}(4449, \cdot)\) n/a 268 1
7120.2.r \(\chi_{7120}(4327, \cdot)\) None 0 2
7120.2.w \(\chi_{7120}(301, \cdot)\) n/a 1440 2
7120.2.x \(\chi_{7120}(3027, \cdot)\) n/a 2112 2
7120.2.y \(\chi_{7120}(1067, \cdot)\) n/a 2152 2
7120.2.z \(\chi_{7120}(589, \cdot)\) n/a 2152 2
7120.2.ba \(\chi_{7120}(3327, \cdot)\) n/a 540 2
7120.2.bd \(\chi_{7120}(2669, \cdot)\) n/a 2152 2
7120.2.bf \(\chi_{7120}(1123, \cdot)\) n/a 2152 2
7120.2.bg \(\chi_{7120}(4683, \cdot)\) n/a 2152 2
7120.2.bj \(\chi_{7120}(1781, \cdot)\) n/a 1408 2
7120.2.bl \(\chi_{7120}(3081, \cdot)\) None 0 2
7120.2.bn \(\chi_{7120}(1423, \cdot)\) n/a 540 2
7120.2.bp \(\chi_{7120}(1247, \cdot)\) n/a 528 2
7120.2.br \(\chi_{7120}(1369, \cdot)\) None 0 2
7120.2.bs \(\chi_{7120}(2081, \cdot)\) n/a 360 2
7120.2.bu \(\chi_{7120}(3383, \cdot)\) None 0 2
7120.2.bw \(\chi_{7120}(4983, \cdot)\) None 0 2
7120.2.by \(\chi_{7120}(2369, \cdot)\) n/a 536 2
7120.2.ca \(\chi_{7120}(1069, \cdot)\) n/a 2112 2
7120.2.cd \(\chi_{7120}(123, \cdot)\) n/a 2152 2
7120.2.ce \(\chi_{7120}(3683, \cdot)\) n/a 2152 2
7120.2.cg \(\chi_{7120}(3381, \cdot)\) n/a 1440 2
7120.2.ci \(\chi_{7120}(767, \cdot)\) n/a 540 2
7120.2.ck \(\chi_{7120}(3861, \cdot)\) n/a 1440 2
7120.2.cl \(\chi_{7120}(1603, \cdot)\) n/a 2112 2
7120.2.cm \(\chi_{7120}(4627, \cdot)\) n/a 2152 2
7120.2.cn \(\chi_{7120}(3149, \cdot)\) n/a 2152 2
7120.2.ct \(\chi_{7120}(2903, \cdot)\) None 0 2
7120.2.cu \(\chi_{7120}(1857, \cdot)\) n/a 1072 4
7120.2.cw \(\chi_{7120}(1031, \cdot)\) None 0 4
7120.2.cx \(\chi_{7120}(279, \cdot)\) None 0 4
7120.2.da \(\chi_{7120}(433, \cdot)\) n/a 1072 4
7120.2.dd \(\chi_{7120}(77, \cdot)\) n/a 4304 4
7120.2.df \(\chi_{7120}(2173, \cdot)\) n/a 4304 4
7120.2.di \(\chi_{7120}(3419, \cdot)\) n/a 4304 4
7120.2.dj \(\chi_{7120}(571, \cdot)\) n/a 2880 4
7120.2.dm \(\chi_{7120}(4131, \cdot)\) n/a 2880 4
7120.2.dn \(\chi_{7120}(2059, \cdot)\) n/a 4304 4
7120.2.dp \(\chi_{7120}(37, \cdot)\) n/a 4304 4
7120.2.dr \(\chi_{7120}(2213, \cdot)\) n/a 4304 4
7120.2.ds \(\chi_{7120}(393, \cdot)\) None 0 4
7120.2.du \(\chi_{7120}(991, \cdot)\) n/a 720 4
7120.2.dv \(\chi_{7120}(319, \cdot)\) n/a 1080 4
7120.2.dy \(\chi_{7120}(1817, \cdot)\) None 0 4
7120.2.ea \(\chi_{7120}(401, \cdot)\) n/a 1800 10
7120.2.eb \(\chi_{7120}(289, \cdot)\) n/a 2680 10
7120.2.eg \(\chi_{7120}(441, \cdot)\) None 0 10
7120.2.eh \(\chi_{7120}(809, \cdot)\) None 0 10
7120.2.ek \(\chi_{7120}(121, \cdot)\) None 0 10
7120.2.el \(\chi_{7120}(489, \cdot)\) None 0 10
7120.2.em \(\chi_{7120}(81, \cdot)\) n/a 1800 10
7120.2.en \(\chi_{7120}(449, \cdot)\) n/a 2680 10
7120.2.eq \(\chi_{7120}(583, \cdot)\) None 0 20
7120.2.ew \(\chi_{7120}(69, \cdot)\) n/a 21520 20
7120.2.ex \(\chi_{7120}(203, \cdot)\) n/a 21520 20
7120.2.ey \(\chi_{7120}(803, \cdot)\) n/a 21520 20
7120.2.ez \(\chi_{7120}(581, \cdot)\) n/a 14400 20
7120.2.fb \(\chi_{7120}(703, \cdot)\) n/a 5400 20
7120.2.fd \(\chi_{7120}(381, \cdot)\) n/a 14400 20
7120.2.ff \(\chi_{7120}(107, \cdot)\) n/a 21520 20
7120.2.fg \(\chi_{7120}(227, \cdot)\) n/a 21520 20
7120.2.fj \(\chi_{7120}(269, \cdot)\) n/a 21520 20
7120.2.fl \(\chi_{7120}(49, \cdot)\) n/a 5360 20
7120.2.fn \(\chi_{7120}(87, \cdot)\) None 0 20
7120.2.fp \(\chi_{7120}(167, \cdot)\) None 0 20
7120.2.fr \(\chi_{7120}(161, \cdot)\) n/a 3600 20
7120.2.fs \(\chi_{7120}(9, \cdot)\) None 0 20
7120.2.fu \(\chi_{7120}(223, \cdot)\) n/a 5400 20
7120.2.fw \(\chi_{7120}(367, \cdot)\) n/a 5400 20
7120.2.fy \(\chi_{7120}(361, \cdot)\) None 0 20
7120.2.ga \(\chi_{7120}(461, \cdot)\) n/a 14400 20
7120.2.gd \(\chi_{7120}(307, \cdot)\) n/a 21520 20
7120.2.ge \(\chi_{7120}(347, \cdot)\) n/a 21520 20
7120.2.gg \(\chi_{7120}(189, \cdot)\) n/a 21520 20
7120.2.gj \(\chi_{7120}(47, \cdot)\) n/a 5400 20
7120.2.gk \(\chi_{7120}(869, \cdot)\) n/a 21520 20
7120.2.gl \(\chi_{7120}(667, \cdot)\) n/a 21520 20
7120.2.gm \(\chi_{7120}(67, \cdot)\) n/a 21520 20
7120.2.gn \(\chi_{7120}(21, \cdot)\) n/a 14400 20
7120.2.gs \(\chi_{7120}(183, \cdot)\) None 0 20
7120.2.gv \(\chi_{7120}(297, \cdot)\) None 0 40
7120.2.gy \(\chi_{7120}(159, \cdot)\) n/a 10800 40
7120.2.gz \(\chi_{7120}(31, \cdot)\) n/a 7200 40
7120.2.hb \(\chi_{7120}(137, \cdot)\) None 0 40
7120.2.hc \(\chi_{7120}(237, \cdot)\) n/a 43040 40
7120.2.he \(\chi_{7120}(197, \cdot)\) n/a 43040 40
7120.2.hg \(\chi_{7120}(19, \cdot)\) n/a 43040 40
7120.2.hh \(\chi_{7120}(51, \cdot)\) n/a 28800 40
7120.2.hk \(\chi_{7120}(211, \cdot)\) n/a 28800 40
7120.2.hl \(\chi_{7120}(59, \cdot)\) n/a 43040 40
7120.2.ho \(\chi_{7120}(13, \cdot)\) n/a 43040 40
7120.2.hq \(\chi_{7120}(213, \cdot)\) n/a 43040 40
7120.2.ht \(\chi_{7120}(33, \cdot)\) n/a 10720 40
7120.2.hw \(\chi_{7120}(119, \cdot)\) None 0 40
7120.2.hx \(\chi_{7120}(151, \cdot)\) None 0 40
7120.2.hz \(\chi_{7120}(193, \cdot)\) n/a 10720 40

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7120))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7120)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(89))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(178))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(356))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(445))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(712))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(890))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1424))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1780))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3560))\)\(^{\oplus 2}\)