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Properties

Label 7104.2
Level 7104
Weight 2
Dimension 588572
Nonzero newspaces 84
Sturm bound 5603328

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Defining parameters

Level: \( N \) = \( 7104 = 2^{6} \cdot 3 \cdot 37 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 84 \)
Sturm bound: \(5603328\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7104))\).

Total New Old
Modular forms 1411200 591652 819548
Cusp forms 1390465 588572 801893
Eisenstein series 20735 3080 17655

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7104))\)

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
7104.2.a \(\chi_{7104}(1, \cdot)\) 7104.2.a.a 1 1
7104.2.a.b 1
7104.2.a.c 1
7104.2.a.d 1
7104.2.a.e 1
7104.2.a.f 1
7104.2.a.g 1
7104.2.a.h 1
7104.2.a.i 1
7104.2.a.j 1
7104.2.a.k 1
7104.2.a.l 1
7104.2.a.m 1
7104.2.a.n 1
7104.2.a.o 1
7104.2.a.p 1
7104.2.a.q 1
7104.2.a.r 1
7104.2.a.s 1
7104.2.a.t 1
7104.2.a.u 1
7104.2.a.v 1
7104.2.a.w 1
7104.2.a.x 1
7104.2.a.y 1
7104.2.a.z 1
7104.2.a.ba 1
7104.2.a.bb 1
7104.2.a.bc 2
7104.2.a.bd 2
7104.2.a.be 2
7104.2.a.bf 2
7104.2.a.bg 2
7104.2.a.bh 2
7104.2.a.bi 2
7104.2.a.bj 2
7104.2.a.bk 2
7104.2.a.bl 2
7104.2.a.bm 2
7104.2.a.bn 2
7104.2.a.bo 3
7104.2.a.bp 3
7104.2.a.bq 3
7104.2.a.br 3
7104.2.a.bs 3
7104.2.a.bt 3
7104.2.a.bu 3
7104.2.a.bv 3
7104.2.a.bw 3
7104.2.a.bx 3
7104.2.a.by 3
7104.2.a.bz 3
7104.2.a.ca 4
7104.2.a.cb 4
7104.2.a.cc 4
7104.2.a.cd 4
7104.2.a.ce 4
7104.2.a.cf 4
7104.2.a.cg 4
7104.2.a.ch 4
7104.2.a.ci 5
7104.2.a.cj 5
7104.2.a.ck 7
7104.2.a.cl 7
7104.2.c \(\chi_{7104}(3551, \cdot)\) n/a 304 1
7104.2.e \(\chi_{7104}(6143, \cdot)\) n/a 288 1
7104.2.f \(\chi_{7104}(3553, \cdot)\) n/a 144 1
7104.2.h \(\chi_{7104}(961, \cdot)\) n/a 152 1
7104.2.j \(\chi_{7104}(2591, \cdot)\) n/a 288 1
7104.2.l \(\chi_{7104}(7103, \cdot)\) n/a 300 1
7104.2.o \(\chi_{7104}(4513, \cdot)\) n/a 152 1
7104.2.q \(\chi_{7104}(5761, \cdot)\) n/a 304 2
7104.2.r \(\chi_{7104}(1745, \cdot)\) n/a 600 2
7104.2.u \(\chi_{7104}(3151, \cdot)\) n/a 304 2
7104.2.v \(\chi_{7104}(31, \cdot)\) n/a 304 2
7104.2.x \(\chi_{7104}(2737, \cdot)\) n/a 304 2
7104.2.ba \(\chi_{7104}(1777, \cdot)\) n/a 288 2
7104.2.bb \(\chi_{7104}(3583, \cdot)\) n/a 304 2
7104.2.be \(\chi_{7104}(5729, \cdot)\) n/a 608 2
7104.2.bf \(\chi_{7104}(815, \cdot)\) n/a 576 2
7104.2.bi \(\chi_{7104}(1775, \cdot)\) n/a 600 2
7104.2.bk \(\chi_{7104}(2177, \cdot)\) n/a 600 2
7104.2.bm \(\chi_{7104}(401, \cdot)\) n/a 600 2
7104.2.bn \(\chi_{7104}(1807, \cdot)\) n/a 304 2
7104.2.bp \(\chi_{7104}(5281, \cdot)\) n/a 304 2
7104.2.bt \(\chi_{7104}(1247, \cdot)\) n/a 608 2
7104.2.bv \(\chi_{7104}(767, \cdot)\) n/a 600 2
7104.2.bx \(\chi_{7104}(2209, \cdot)\) n/a 304 2
7104.2.bz \(\chi_{7104}(1729, \cdot)\) n/a 304 2
7104.2.ca \(\chi_{7104}(4319, \cdot)\) n/a 608 2
7104.2.cc \(\chi_{7104}(4799, \cdot)\) n/a 600 2
7104.2.cg \(\chi_{7104}(887, \cdot)\) None 0 4
7104.2.ch \(\chi_{7104}(889, \cdot)\) None 0 4
7104.2.ck \(\chi_{7104}(857, \cdot)\) None 0 4
7104.2.cl \(\chi_{7104}(487, \cdot)\) None 0 4
7104.2.co \(\chi_{7104}(2263, \cdot)\) None 0 4
7104.2.cp \(\chi_{7104}(2633, \cdot)\) None 0 4
7104.2.cq \(\chi_{7104}(1703, \cdot)\) None 0 4
7104.2.cr \(\chi_{7104}(73, \cdot)\) None 0 4
7104.2.cu \(\chi_{7104}(1921, \cdot)\) n/a 912 6
7104.2.cw \(\chi_{7104}(2095, \cdot)\) n/a 608 4
7104.2.cx \(\chi_{7104}(689, \cdot)\) n/a 1200 4
7104.2.cz \(\chi_{7104}(2465, \cdot)\) n/a 1216 4
7104.2.dc \(\chi_{7104}(2543, \cdot)\) n/a 1200 4
7104.2.dd \(\chi_{7104}(47, \cdot)\) n/a 1200 4
7104.2.df \(\chi_{7104}(2561, \cdot)\) n/a 1200 4
7104.2.di \(\chi_{7104}(415, \cdot)\) n/a 608 4
7104.2.dk \(\chi_{7104}(433, \cdot)\) n/a 608 4
7104.2.dl \(\chi_{7104}(529, \cdot)\) n/a 608 4
7104.2.do \(\chi_{7104}(319, \cdot)\) n/a 608 4
7104.2.dp \(\chi_{7104}(2191, \cdot)\) n/a 608 4
7104.2.ds \(\chi_{7104}(785, \cdot)\) n/a 1200 4
7104.2.dt \(\chi_{7104}(475, \cdot)\) n/a 4864 8
7104.2.dv \(\chi_{7104}(845, \cdot)\) n/a 9696 8
7104.2.dx \(\chi_{7104}(443, \cdot)\) n/a 9696 8
7104.2.dz \(\chi_{7104}(445, \cdot)\) n/a 4608 8
7104.2.eb \(\chi_{7104}(371, \cdot)\) n/a 9216 8
7104.2.ed \(\chi_{7104}(517, \cdot)\) n/a 4864 8
7104.2.eg \(\chi_{7104}(43, \cdot)\) n/a 4864 8
7104.2.ei \(\chi_{7104}(413, \cdot)\) n/a 9696 8
7104.2.ek \(\chi_{7104}(959, \cdot)\) n/a 1800 6
7104.2.en \(\chi_{7104}(1151, \cdot)\) n/a 1800 6
7104.2.eo \(\chi_{7104}(2113, \cdot)\) n/a 912 6
7104.2.er \(\chi_{7104}(863, \cdot)\) n/a 1824 6
7104.2.es \(\chi_{7104}(673, \cdot)\) n/a 912 6
7104.2.ev \(\chi_{7104}(289, \cdot)\) n/a 912 6
7104.2.ew \(\chi_{7104}(95, \cdot)\) n/a 1824 6
7104.2.ey \(\chi_{7104}(841, \cdot)\) None 0 8
7104.2.ez \(\chi_{7104}(359, \cdot)\) None 0 8
7104.2.fe \(\chi_{7104}(1879, \cdot)\) None 0 8
7104.2.ff \(\chi_{7104}(2249, \cdot)\) None 0 8
7104.2.fi \(\chi_{7104}(473, \cdot)\) None 0 8
7104.2.fj \(\chi_{7104}(103, \cdot)\) None 0 8
7104.2.fm \(\chi_{7104}(121, \cdot)\) None 0 8
7104.2.fn \(\chi_{7104}(455, \cdot)\) None 0 8
7104.2.fq \(\chi_{7104}(257, \cdot)\) n/a 3600 12
7104.2.fr \(\chi_{7104}(1663, \cdot)\) n/a 1824 12
7104.2.fs \(\chi_{7104}(337, \cdot)\) n/a 1824 12
7104.2.fu \(\chi_{7104}(1103, \cdot)\) n/a 3600 12
7104.2.fw \(\chi_{7104}(209, \cdot)\) n/a 3600 12
7104.2.fx \(\chi_{7104}(1615, \cdot)\) n/a 1824 12
7104.2.gc \(\chi_{7104}(17, \cdot)\) n/a 3600 12
7104.2.gd \(\chi_{7104}(79, \cdot)\) n/a 1824 12
7104.2.ge \(\chi_{7104}(527, \cdot)\) n/a 3600 12
7104.2.gg \(\chi_{7104}(49, \cdot)\) n/a 1824 12
7104.2.gk \(\chi_{7104}(607, \cdot)\) n/a 1824 12
7104.2.gl \(\chi_{7104}(161, \cdot)\) n/a 3648 12
7104.2.gm \(\chi_{7104}(917, \cdot)\) n/a 19392 16
7104.2.go \(\chi_{7104}(547, \cdot)\) n/a 9728 16
7104.2.gr \(\chi_{7104}(565, \cdot)\) n/a 9728 16
7104.2.gt \(\chi_{7104}(11, \cdot)\) n/a 19392 16
7104.2.gv \(\chi_{7104}(85, \cdot)\) n/a 9728 16
7104.2.gx \(\chi_{7104}(491, \cdot)\) n/a 19392 16
7104.2.gz \(\chi_{7104}(29, \cdot)\) n/a 19392 16
7104.2.hb \(\chi_{7104}(1435, \cdot)\) n/a 9728 16
7104.2.hc \(\chi_{7104}(535, \cdot)\) None 0 24
7104.2.hd \(\chi_{7104}(89, \cdot)\) None 0 24
7104.2.hi \(\chi_{7104}(71, \cdot)\) None 0 24
7104.2.hj \(\chi_{7104}(25, \cdot)\) None 0 24
7104.2.hm \(\chi_{7104}(601, \cdot)\) None 0 24
7104.2.hn \(\chi_{7104}(215, \cdot)\) None 0 24
7104.2.ho \(\chi_{7104}(281, \cdot)\) None 0 24
7104.2.hp \(\chi_{7104}(55, \cdot)\) None 0 24
7104.2.hs \(\chi_{7104}(299, \cdot)\) n/a 58176 48
7104.2.hv \(\chi_{7104}(157, \cdot)\) n/a 29184 48
7104.2.hx \(\chi_{7104}(461, \cdot)\) n/a 58176 48
7104.2.hz \(\chi_{7104}(5, \cdot)\) n/a 58176 48
7104.2.ia \(\chi_{7104}(91, \cdot)\) n/a 29184 48
7104.2.ic \(\chi_{7104}(19, \cdot)\) n/a 29184 48
7104.2.ie \(\chi_{7104}(373, \cdot)\) n/a 29184 48
7104.2.ih \(\chi_{7104}(83, \cdot)\) n/a 58176 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7104))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7104)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 28}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(111))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(148))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(222))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(296))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(444))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(592))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(888))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1184))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1776))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2368))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3552))\)\(^{\oplus 2}\)