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Properties

Label 22542.2
Level 22542
Weight 2
Dimension 3430268
Nonzero newspaces 72
Sturm bound 55931904

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Defining parameters

Level: \( N \) = \( 22542 = 2 \cdot 3 \cdot 13 \cdot 17^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 72 \)
Sturm bound: \(55931904\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(22542))\).

Total New Old
Modular forms 14021376 3430268 10591108
Cusp forms 13944577 3430268 10514309
Eisenstein series 76799 0 76799

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(22542))\)

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
22542.2.a \(\chi_{22542}(1, \cdot)\) 22542.2.a.a 1 1
22542.2.a.b 1
22542.2.a.c 1
22542.2.a.d 1
22542.2.a.e 1
22542.2.a.f 1
22542.2.a.g 1
22542.2.a.h 1
22542.2.a.i 1
22542.2.a.j 1
22542.2.a.k 1
22542.2.a.l 1
22542.2.a.m 1
22542.2.a.n 1
22542.2.a.o 1
22542.2.a.p 1
22542.2.a.q 1
22542.2.a.r 1
22542.2.a.s 1
22542.2.a.t 1
22542.2.a.u 1
22542.2.a.v 1
22542.2.a.w 1
22542.2.a.x 1
22542.2.a.y 1
22542.2.a.z 1
22542.2.a.ba 2
22542.2.a.bb 2
22542.2.a.bc 2
22542.2.a.bd 2
22542.2.a.be 2
22542.2.a.bf 2
22542.2.a.bg 2
22542.2.a.bh 2
22542.2.a.bi 2
22542.2.a.bj 2
22542.2.a.bk 3
22542.2.a.bl 3
22542.2.a.bm 3
22542.2.a.bn 3
22542.2.a.bo 3
22542.2.a.bp 3
22542.2.a.bq 3
22542.2.a.br 3
22542.2.a.bs 3
22542.2.a.bt 3
22542.2.a.bu 3
22542.2.a.bv 3
22542.2.a.bw 3
22542.2.a.bx 4
22542.2.a.by 4
22542.2.a.bz 4
22542.2.a.ca 4
22542.2.a.cb 4
22542.2.a.cc 4
22542.2.a.cd 4
22542.2.a.ce 4
22542.2.a.cf 4
22542.2.a.cg 4
22542.2.a.ch 4
22542.2.a.ci 5
22542.2.a.cj 5
22542.2.a.ck 5
22542.2.a.cl 5
22542.2.a.cm 5
22542.2.a.cn 6
22542.2.a.co 6
22542.2.a.cp 6
22542.2.a.cq 6
22542.2.a.cr 8
22542.2.a.cs 8
22542.2.a.ct 9
22542.2.a.cu 9
22542.2.a.cv 9
22542.2.a.cw 9
22542.2.a.cx 10
22542.2.a.cy 10
22542.2.a.cz 12
22542.2.a.da 12
22542.2.a.db 12
22542.2.a.dc 12
22542.2.a.dd 12
22542.2.a.de 12
22542.2.a.df 12
22542.2.a.dg 12
22542.2.a.dh 15
22542.2.a.di 15
22542.2.a.dj 15
22542.2.a.dk 15
22542.2.a.dl 16
22542.2.a.dm 16
22542.2.a.dn 16
22542.2.a.do 16
22542.2.a.dp 16
22542.2.a.dq 16
22542.2.a.dr 20
22542.2.a.ds 20
22542.2.b \(\chi_{22542}(17341, \cdot)\) n/a 630 1
22542.2.c \(\chi_{22542}(12715, \cdot)\) n/a 540 1
22542.2.h \(\chi_{22542}(7513, \cdot)\) n/a 628 1
22542.2.i \(\chi_{22542}(5203, \cdot)\) n/a 1268 2
22542.2.k \(\chi_{22542}(905, \cdot)\) n/a 2520 2
22542.2.m \(\chi_{22542}(1483, \cdot)\) n/a 1080 2
22542.2.n \(\chi_{22542}(12137, \cdot)\) n/a 2520 2
22542.2.p \(\chi_{22542}(2891, \cdot)\) n/a 2532 2
22542.2.s \(\chi_{22542}(6031, \cdot)\) n/a 1256 2
22542.2.t \(\chi_{22542}(4373, \cdot)\) n/a 2520 2
22542.2.x \(\chi_{22542}(10981, \cdot)\) n/a 1264 2
22542.2.y \(\chi_{22542}(12139, \cdot)\) n/a 1264 2
22542.2.z \(\chi_{22542}(2311, \cdot)\) n/a 1256 2
22542.2.bc \(\chi_{22542}(12293, \cdot)\) n/a 5040 4
22542.2.bg \(\chi_{22542}(12871, \cdot)\) n/a 2160 4
22542.2.bh \(\chi_{22542}(7669, \cdot)\) n/a 2528 4
22542.2.bi \(\chi_{22542}(2735, \cdot)\) n/a 5040 4
22542.2.bk \(\chi_{22542}(5453, \cdot)\) n/a 5040 4
22542.2.bm \(\chi_{22542}(829, \cdot)\) n/a 2512 4
22542.2.bp \(\chi_{22542}(6359, \cdot)\) n/a 5056 4
22542.2.br \(\chi_{22542}(6935, \cdot)\) n/a 5040 4
22542.2.bs \(\chi_{22542}(6685, \cdot)\) n/a 2528 4
22542.2.bv \(\chi_{22542}(7187, \cdot)\) n/a 5040 4
22542.2.bx \(\chi_{22542}(131, \cdot)\) n/a 8640 8
22542.2.by \(\chi_{22542}(1091, \cdot)\) n/a 10080 8
22542.2.ca \(\chi_{22542}(1669, \cdot)\) n/a 5040 8
22542.2.cd \(\chi_{22542}(5845, \cdot)\) n/a 5040 8
22542.2.ce \(\chi_{22542}(1327, \cdot)\) n/a 9792 16
22542.2.cg \(\chi_{22542}(2711, \cdot)\) n/a 10080 8
22542.2.ch \(\chi_{22542}(757, \cdot)\) n/a 5024 8
22542.2.ci \(\chi_{22542}(2467, \cdot)\) n/a 5056 8
22542.2.cm \(\chi_{22542}(977, \cdot)\) n/a 10080 8
22542.2.cn \(\chi_{22542}(883, \cdot)\) n/a 11456 16
22542.2.cs \(\chi_{22542}(781, \cdot)\) n/a 9792 16
22542.2.ct \(\chi_{22542}(103, \cdot)\) n/a 11456 16
22542.2.cu \(\chi_{22542}(643, \cdot)\) n/a 10080 16
22542.2.cx \(\chi_{22542}(709, \cdot)\) n/a 10080 16
22542.2.cz \(\chi_{22542}(329, \cdot)\) n/a 20160 16
22542.2.da \(\chi_{22542}(503, \cdot)\) n/a 20160 16
22542.2.dc \(\chi_{22542}(919, \cdot)\) n/a 22784 32
22542.2.de \(\chi_{22542}(47, \cdot)\) n/a 45696 32
22542.2.df \(\chi_{22542}(259, \cdot)\) n/a 22912 32
22542.2.di \(\chi_{22542}(239, \cdot)\) n/a 45696 32
22542.2.dk \(\chi_{22542}(203, \cdot)\) n/a 45696 32
22542.2.dl \(\chi_{22542}(157, \cdot)\) n/a 19584 32
22542.2.dn \(\chi_{22542}(863, \cdot)\) n/a 45696 32
22542.2.dr \(\chi_{22542}(985, \cdot)\) n/a 22912 32
22542.2.ds \(\chi_{22542}(205, \cdot)\) n/a 22912 32
22542.2.dt \(\chi_{22542}(373, \cdot)\) n/a 22784 32
22542.2.dx \(\chi_{22542}(83, \cdot)\) n/a 91392 64
22542.2.dy \(\chi_{22542}(25, \cdot)\) n/a 45568 64
22542.2.dz \(\chi_{22542}(859, \cdot)\) n/a 39168 64
22542.2.ed \(\chi_{22542}(161, \cdot)\) n/a 91392 64
22542.2.ee \(\chi_{22542}(557, \cdot)\) n/a 91392 64
22542.2.eh \(\chi_{22542}(55, \cdot)\) n/a 45568 64
22542.2.ei \(\chi_{22542}(305, \cdot)\) n/a 91392 64
22542.2.ek \(\chi_{22542}(137, \cdot)\) n/a 91392 64
22542.2.en \(\chi_{22542}(361, \cdot)\) n/a 45824 64
22542.2.ep \(\chi_{22542}(89, \cdot)\) n/a 91392 64
22542.2.eq \(\chi_{22542}(73, \cdot)\) n/a 91392 128
22542.2.et \(\chi_{22542}(31, \cdot)\) n/a 91392 128
22542.2.ev \(\chi_{22542}(233, \cdot)\) n/a 182784 128
22542.2.ew \(\chi_{22542}(209, \cdot)\) n/a 156672 128
22542.2.ey \(\chi_{22542}(383, \cdot)\) n/a 182784 128
22542.2.fc \(\chi_{22542}(43, \cdot)\) n/a 91136 128
22542.2.fd \(\chi_{22542}(451, \cdot)\) n/a 91648 128
22542.2.fe \(\chi_{22542}(59, \cdot)\) n/a 182784 128
22542.2.fh \(\chi_{22542}(29, \cdot)\) n/a 365568 256
22542.2.fi \(\chi_{22542}(23, \cdot)\) n/a 365568 256
22542.2.fk \(\chi_{22542}(37, \cdot)\) n/a 182784 256
22542.2.fn \(\chi_{22542}(7, \cdot)\) n/a 182784 256

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(22542))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(22542)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(221))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(289))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(442))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(578))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(663))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(867))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1326))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1734))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3757))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7514))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11271))\)\(^{\oplus 2}\)