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Properties

Label 7623.2
Level 7623
Weight 2
Dimension 1553877
Nonzero newspaces 80
Sturm bound 8363520

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Defining parameters

Level: \( N \) = \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 80 \)
Sturm bound: \(8363520\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7623))\).

Total New Old
Modular forms 2106240 1566521 539719
Cusp forms 2075521 1553877 521644
Eisenstein series 30719 12644 18075

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7623))\)

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
7623.2.a \(\chi_{7623}(1, \cdot)\) 7623.2.a.a 1 1
7623.2.a.b 1
7623.2.a.c 1
7623.2.a.d 1
7623.2.a.e 1
7623.2.a.f 1
7623.2.a.g 1
7623.2.a.h 1
7623.2.a.i 1
7623.2.a.j 1
7623.2.a.k 1
7623.2.a.l 1
7623.2.a.m 1
7623.2.a.n 1
7623.2.a.o 1
7623.2.a.p 1
7623.2.a.q 1
7623.2.a.r 1
7623.2.a.s 1
7623.2.a.t 2
7623.2.a.u 2
7623.2.a.v 2
7623.2.a.w 2
7623.2.a.x 2
7623.2.a.y 2
7623.2.a.z 2
7623.2.a.ba 2
7623.2.a.bb 2
7623.2.a.bc 2
7623.2.a.bd 2
7623.2.a.be 2
7623.2.a.bf 2
7623.2.a.bg 2
7623.2.a.bh 2
7623.2.a.bi 2
7623.2.a.bj 2
7623.2.a.bk 2
7623.2.a.bl 2
7623.2.a.bm 2
7623.2.a.bn 2
7623.2.a.bo 2
7623.2.a.bp 2
7623.2.a.bq 2
7623.2.a.br 2
7623.2.a.bs 2
7623.2.a.bt 2
7623.2.a.bu 2
7623.2.a.bv 2
7623.2.a.bw 2
7623.2.a.bx 2
7623.2.a.by 2
7623.2.a.bz 3
7623.2.a.ca 3
7623.2.a.cb 3
7623.2.a.cc 3
7623.2.a.cd 3
7623.2.a.ce 3
7623.2.a.cf 4
7623.2.a.cg 4
7623.2.a.ch 4
7623.2.a.ci 4
7623.2.a.cj 4
7623.2.a.ck 4
7623.2.a.cl 4
7623.2.a.cm 4
7623.2.a.cn 4
7623.2.a.co 4
7623.2.a.cp 6
7623.2.a.cq 6
7623.2.a.cr 6
7623.2.a.cs 6
7623.2.a.ct 8
7623.2.a.cu 8
7623.2.a.cv 8
7623.2.a.cw 8
7623.2.a.cx 10
7623.2.a.cy 10
7623.2.a.cz 12
7623.2.a.da 12
7623.2.a.db 16
7623.2.a.dc 16
7623.2.c \(\chi_{7623}(1693, \cdot)\) n/a 352 1
7623.2.e \(\chi_{7623}(1574, \cdot)\) n/a 292 1
7623.2.g \(\chi_{7623}(4355, \cdot)\) n/a 216 1
7623.2.i \(\chi_{7623}(2179, \cdot)\) n/a 708 2
7623.2.j \(\chi_{7623}(2542, \cdot)\) n/a 1308 2
7623.2.k \(\chi_{7623}(1453, \cdot)\) n/a 1708 2
7623.2.l \(\chi_{7623}(3994, \cdot)\) n/a 1708 2
7623.2.m \(\chi_{7623}(1576, \cdot)\) n/a 1080 4
7623.2.n \(\chi_{7623}(4478, \cdot)\) n/a 1708 2
7623.2.p \(\chi_{7623}(241, \cdot)\) n/a 1696 2
7623.2.r \(\chi_{7623}(725, \cdot)\) n/a 1696 2
7623.2.w \(\chi_{7623}(1814, \cdot)\) n/a 1296 2
7623.2.x \(\chi_{7623}(3266, \cdot)\) n/a 576 2
7623.2.ba \(\chi_{7623}(4597, \cdot)\) n/a 1696 2
7623.2.bd \(\chi_{7623}(4115, \cdot)\) n/a 1708 2
7623.2.be \(\chi_{7623}(2663, \cdot)\) n/a 580 2
7623.2.bg \(\chi_{7623}(2782, \cdot)\) n/a 704 2
7623.2.bj \(\chi_{7623}(4234, \cdot)\) n/a 1696 2
7623.2.bk \(\chi_{7623}(122, \cdot)\) n/a 1708 2
7623.2.bn \(\chi_{7623}(3992, \cdot)\) n/a 1696 2
7623.2.bq \(\chi_{7623}(2339, \cdot)\) n/a 864 4
7623.2.bs \(\chi_{7623}(251, \cdot)\) n/a 1152 4
7623.2.bu \(\chi_{7623}(118, \cdot)\) n/a 1408 4
7623.2.bw \(\chi_{7623}(694, \cdot)\) n/a 3300 10
7623.2.bx \(\chi_{7623}(1600, \cdot)\) n/a 6784 8
7623.2.by \(\chi_{7623}(130, \cdot)\) n/a 6784 8
7623.2.bz \(\chi_{7623}(487, \cdot)\) n/a 2816 8
7623.2.ca \(\chi_{7623}(148, \cdot)\) n/a 5184 8
7623.2.cc \(\chi_{7623}(197, \cdot)\) n/a 2640 10
7623.2.ce \(\chi_{7623}(188, \cdot)\) n/a 3520 10
7623.2.cg \(\chi_{7623}(307, \cdot)\) n/a 4380 10
7623.2.cj \(\chi_{7623}(578, \cdot)\) n/a 6784 8
7623.2.cm \(\chi_{7623}(614, \cdot)\) n/a 6784 8
7623.2.co \(\chi_{7623}(766, \cdot)\) n/a 2816 8
7623.2.cp \(\chi_{7623}(475, \cdot)\) n/a 6784 8
7623.2.cr \(\chi_{7623}(608, \cdot)\) n/a 6784 8
7623.2.cu \(\chi_{7623}(269, \cdot)\) n/a 2304 8
7623.2.cw \(\chi_{7623}(94, \cdot)\) n/a 6784 8
7623.2.cy \(\chi_{7623}(239, \cdot)\) n/a 5184 8
7623.2.db \(\chi_{7623}(233, \cdot)\) n/a 2304 8
7623.2.df \(\chi_{7623}(2048, \cdot)\) n/a 6784 8
7623.2.dh \(\chi_{7623}(40, \cdot)\) n/a 6784 8
7623.2.dj \(\chi_{7623}(2084, \cdot)\) n/a 6784 8
7623.2.dk \(\chi_{7623}(529, \cdot)\) n/a 21040 20
7623.2.dl \(\chi_{7623}(67, \cdot)\) n/a 21040 20
7623.2.dm \(\chi_{7623}(232, \cdot)\) n/a 15840 20
7623.2.dn \(\chi_{7623}(100, \cdot)\) n/a 8760 20
7623.2.do \(\chi_{7623}(64, \cdot)\) n/a 13200 40
7623.2.dq \(\chi_{7623}(263, \cdot)\) n/a 21040 20
7623.2.dt \(\chi_{7623}(551, \cdot)\) n/a 21040 20
7623.2.du \(\chi_{7623}(76, \cdot)\) n/a 21040 20
7623.2.dx \(\chi_{7623}(10, \cdot)\) n/a 8760 20
7623.2.dz \(\chi_{7623}(89, \cdot)\) n/a 7040 20
7623.2.ea \(\chi_{7623}(419, \cdot)\) n/a 21040 20
7623.2.ed \(\chi_{7623}(439, \cdot)\) n/a 21040 20
7623.2.eg \(\chi_{7623}(296, \cdot)\) n/a 7040 20
7623.2.eh \(\chi_{7623}(428, \cdot)\) n/a 15840 20
7623.2.em \(\chi_{7623}(32, \cdot)\) n/a 21040 20
7623.2.eo \(\chi_{7623}(670, \cdot)\) n/a 21040 20
7623.2.eq \(\chi_{7623}(320, \cdot)\) n/a 21040 20
7623.2.es \(\chi_{7623}(244, \cdot)\) n/a 17520 40
7623.2.eu \(\chi_{7623}(125, \cdot)\) n/a 14080 40
7623.2.ew \(\chi_{7623}(8, \cdot)\) n/a 10560 40
7623.2.ey \(\chi_{7623}(169, \cdot)\) n/a 63360 80
7623.2.ez \(\chi_{7623}(37, \cdot)\) n/a 35040 80
7623.2.fa \(\chi_{7623}(4, \cdot)\) n/a 84160 80
7623.2.fb \(\chi_{7623}(25, \cdot)\) n/a 84160 80
7623.2.fc \(\chi_{7623}(5, \cdot)\) n/a 84160 80
7623.2.fe \(\chi_{7623}(52, \cdot)\) n/a 84160 80
7623.2.fg \(\chi_{7623}(2, \cdot)\) n/a 84160 80
7623.2.fk \(\chi_{7623}(107, \cdot)\) n/a 28160 80
7623.2.fn \(\chi_{7623}(29, \cdot)\) n/a 63360 80
7623.2.fp \(\chi_{7623}(61, \cdot)\) n/a 84160 80
7623.2.fr \(\chi_{7623}(26, \cdot)\) n/a 28160 80
7623.2.fu \(\chi_{7623}(20, \cdot)\) n/a 84160 80
7623.2.fw \(\chi_{7623}(13, \cdot)\) n/a 84160 80
7623.2.fx \(\chi_{7623}(19, \cdot)\) n/a 35040 80
7623.2.fz \(\chi_{7623}(47, \cdot)\) n/a 84160 80
7623.2.gc \(\chi_{7623}(74, \cdot)\) n/a 84160 80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7623))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7623)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(231))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(693))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(847))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1089))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2541))\)\(^{\oplus 2}\)