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Properties

Label 7605.2
Level 7605
Weight 2
Dimension 1460457
Nonzero newspaces 100
Sturm bound 8176896

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Defining parameters

Level: \( N \) = \( 7605 = 3^{2} \cdot 5 \cdot 13^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 100 \)
Sturm bound: \(8176896\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7605))\).

Total New Old
Modular forms 2058816 1471499 587317
Cusp forms 2029633 1460457 569176
Eisenstein series 29183 11042 18141

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7605))\)

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
7605.2.a \(\chi_{7605}(1, \cdot)\) 7605.2.a.a 1 1
7605.2.a.b 1
7605.2.a.c 1
7605.2.a.d 1
7605.2.a.e 1
7605.2.a.f 1
7605.2.a.g 1
7605.2.a.h 1
7605.2.a.i 1
7605.2.a.j 1
7605.2.a.k 1
7605.2.a.l 1
7605.2.a.m 1
7605.2.a.n 1
7605.2.a.o 1
7605.2.a.p 1
7605.2.a.q 1
7605.2.a.r 1
7605.2.a.s 1
7605.2.a.t 1
7605.2.a.u 1
7605.2.a.v 1
7605.2.a.w 2
7605.2.a.x 2
7605.2.a.y 2
7605.2.a.z 2
7605.2.a.ba 2
7605.2.a.bb 2
7605.2.a.bc 2
7605.2.a.bd 2
7605.2.a.be 2
7605.2.a.bf 2
7605.2.a.bg 2
7605.2.a.bh 2
7605.2.a.bi 2
7605.2.a.bj 2
7605.2.a.bk 2
7605.2.a.bl 2
7605.2.a.bm 3
7605.2.a.bn 3
7605.2.a.bo 3
7605.2.a.bp 3
7605.2.a.bq 3
7605.2.a.br 3
7605.2.a.bs 3
7605.2.a.bt 3
7605.2.a.bu 3
7605.2.a.bv 3
7605.2.a.bw 3
7605.2.a.bx 3
7605.2.a.by 3
7605.2.a.bz 3
7605.2.a.ca 3
7605.2.a.cb 3
7605.2.a.cc 3
7605.2.a.cd 3
7605.2.a.ce 3
7605.2.a.cf 4
7605.2.a.cg 4
7605.2.a.ch 4
7605.2.a.ci 4
7605.2.a.cj 4
7605.2.a.ck 4
7605.2.a.cl 5
7605.2.a.cm 5
7605.2.a.cn 5
7605.2.a.co 5
7605.2.a.cp 9
7605.2.a.cq 9
7605.2.a.cr 9
7605.2.a.cs 9
7605.2.a.ct 10
7605.2.a.cu 10
7605.2.a.cv 12
7605.2.a.cw 12
7605.2.a.cx 12
7605.2.a.cy 12
7605.2.b \(\chi_{7605}(1351, \cdot)\) n/a 258 1
7605.2.c \(\chi_{7605}(4564, \cdot)\) n/a 376 1
7605.2.h \(\chi_{7605}(5914, \cdot)\) n/a 376 1
7605.2.i \(\chi_{7605}(2536, \cdot)\) n/a 1240 2
7605.2.j \(\chi_{7605}(991, \cdot)\) n/a 512 2
7605.2.k \(\chi_{7605}(3571, \cdot)\) n/a 1232 2
7605.2.l \(\chi_{7605}(3526, \cdot)\) n/a 1232 2
7605.2.n \(\chi_{7605}(2098, \cdot)\) n/a 750 2
7605.2.p \(\chi_{7605}(3212, \cdot)\) n/a 620 2
7605.2.q \(\chi_{7605}(944, \cdot)\) n/a 616 2
7605.2.r \(\chi_{7605}(746, \cdot)\) n/a 416 2
7605.2.v \(\chi_{7605}(4562, \cdot)\) n/a 616 2
7605.2.w \(\chi_{7605}(577, \cdot)\) n/a 750 2
7605.2.ba \(\chi_{7605}(2896, \cdot)\) n/a 1232 2
7605.2.bb \(\chi_{7605}(484, \cdot)\) n/a 1808 2
7605.2.be \(\chi_{7605}(844, \cdot)\) n/a 1808 2
7605.2.bf \(\chi_{7605}(4879, \cdot)\) n/a 752 2
7605.2.bk \(\chi_{7605}(2389, \cdot)\) n/a 1808 2
7605.2.bl \(\chi_{7605}(529, \cdot)\) n/a 1808 2
7605.2.bm \(\chi_{7605}(2851, \cdot)\) n/a 1232 2
7605.2.br \(\chi_{7605}(2029, \cdot)\) n/a 1816 2
7605.2.bs \(\chi_{7605}(5554, \cdot)\) n/a 748 2
7605.2.bt \(\chi_{7605}(3886, \cdot)\) n/a 1232 2
7605.2.bu \(\chi_{7605}(316, \cdot)\) n/a 512 2
7605.2.bx \(\chi_{7605}(2344, \cdot)\) n/a 1808 2
7605.2.ca \(\chi_{7605}(3568, \cdot)\) n/a 3616 4
7605.2.cc \(\chi_{7605}(1948, \cdot)\) n/a 3616 4
7605.2.cf \(\chi_{7605}(1333, \cdot)\) n/a 1500 4
7605.2.cg \(\chi_{7605}(268, \cdot)\) n/a 3616 4
7605.2.ci \(\chi_{7605}(698, \cdot)\) n/a 3616 4
7605.2.cm \(\chi_{7605}(596, \cdot)\) n/a 2464 4
7605.2.cn \(\chi_{7605}(3629, \cdot)\) n/a 3616 4
7605.2.co \(\chi_{7605}(1037, \cdot)\) n/a 3616 4
7605.2.cr \(\chi_{7605}(23, \cdot)\) n/a 3616 4
7605.2.cs \(\chi_{7605}(1013, \cdot)\) n/a 3616 4
7605.2.cv \(\chi_{7605}(3527, \cdot)\) n/a 1232 4
7605.2.cw \(\chi_{7605}(1601, \cdot)\) n/a 816 4
7605.2.cx \(\chi_{7605}(89, \cdot)\) n/a 1232 4
7605.2.dc \(\chi_{7605}(239, \cdot)\) n/a 3616 4
7605.2.dd \(\chi_{7605}(2216, \cdot)\) n/a 2464 4
7605.2.de \(\chi_{7605}(1094, \cdot)\) n/a 3616 4
7605.2.df \(\chi_{7605}(1451, \cdot)\) n/a 2464 4
7605.2.dj \(\chi_{7605}(677, \cdot)\) n/a 3632 4
7605.2.dk \(\chi_{7605}(653, \cdot)\) n/a 3616 4
7605.2.dn \(\chi_{7605}(4202, \cdot)\) n/a 1232 4
7605.2.dp \(\chi_{7605}(2953, \cdot)\) n/a 1500 4
7605.2.dq \(\chi_{7605}(1282, \cdot)\) n/a 3616 4
7605.2.dt \(\chi_{7605}(418, \cdot)\) n/a 3616 4
7605.2.dv \(\chi_{7605}(2047, \cdot)\) n/a 3616 4
7605.2.dw \(\chi_{7605}(586, \cdot)\) n/a 3624 12
7605.2.dx \(\chi_{7605}(64, \cdot)\) n/a 5424 12
7605.2.ec \(\chi_{7605}(469, \cdot)\) n/a 5448 12
7605.2.ed \(\chi_{7605}(181, \cdot)\) n/a 3624 12
7605.2.ee \(\chi_{7605}(16, \cdot)\) n/a 17472 24
7605.2.ef \(\chi_{7605}(61, \cdot)\) n/a 17472 24
7605.2.eg \(\chi_{7605}(406, \cdot)\) n/a 7296 24
7605.2.eh \(\chi_{7605}(196, \cdot)\) n/a 17472 24
7605.2.ej \(\chi_{7605}(73, \cdot)\) n/a 10872 24
7605.2.ek \(\chi_{7605}(233, \cdot)\) n/a 8736 24
7605.2.eo \(\chi_{7605}(161, \cdot)\) n/a 5760 24
7605.2.ep \(\chi_{7605}(44, \cdot)\) n/a 8736 24
7605.2.eq \(\chi_{7605}(53, \cdot)\) n/a 8736 24
7605.2.es \(\chi_{7605}(307, \cdot)\) n/a 10872 24
7605.2.ew \(\chi_{7605}(4, \cdot)\) n/a 26112 24
7605.2.ez \(\chi_{7605}(901, \cdot)\) n/a 7296 24
7605.2.fa \(\chi_{7605}(376, \cdot)\) n/a 17472 24
7605.2.fb \(\chi_{7605}(289, \cdot)\) n/a 10896 24
7605.2.fc \(\chi_{7605}(79, \cdot)\) n/a 26112 24
7605.2.fh \(\chi_{7605}(166, \cdot)\) n/a 17472 24
7605.2.fi \(\chi_{7605}(94, \cdot)\) n/a 26112 24
7605.2.fj \(\chi_{7605}(49, \cdot)\) n/a 26112 24
7605.2.fo \(\chi_{7605}(199, \cdot)\) n/a 10848 24
7605.2.fp \(\chi_{7605}(259, \cdot)\) n/a 26112 24
7605.2.fs \(\chi_{7605}(139, \cdot)\) n/a 26112 24
7605.2.ft \(\chi_{7605}(121, \cdot)\) n/a 17472 24
7605.2.fw \(\chi_{7605}(292, \cdot)\) n/a 52224 48
7605.2.fy \(\chi_{7605}(7, \cdot)\) n/a 52224 48
7605.2.gb \(\chi_{7605}(112, \cdot)\) n/a 52224 48
7605.2.gc \(\chi_{7605}(28, \cdot)\) n/a 21744 48
7605.2.ge \(\chi_{7605}(107, \cdot)\) n/a 17472 48
7605.2.gh \(\chi_{7605}(92, \cdot)\) n/a 52224 48
7605.2.gi \(\chi_{7605}(68, \cdot)\) n/a 52224 48
7605.2.gm \(\chi_{7605}(86, \cdot)\) n/a 34944 48
7605.2.gn \(\chi_{7605}(254, \cdot)\) n/a 52224 48
7605.2.go \(\chi_{7605}(41, \cdot)\) n/a 34944 48
7605.2.gp \(\chi_{7605}(164, \cdot)\) n/a 52224 48
7605.2.gu \(\chi_{7605}(314, \cdot)\) n/a 17472 48
7605.2.gv \(\chi_{7605}(71, \cdot)\) n/a 11712 48
7605.2.gw \(\chi_{7605}(17, \cdot)\) n/a 17472 48
7605.2.gz \(\chi_{7605}(173, \cdot)\) n/a 52224 48
7605.2.ha \(\chi_{7605}(38, \cdot)\) n/a 52224 48
7605.2.hd \(\chi_{7605}(212, \cdot)\) n/a 52224 48
7605.2.he \(\chi_{7605}(59, \cdot)\) n/a 52224 48
7605.2.hf \(\chi_{7605}(11, \cdot)\) n/a 34944 48
7605.2.hj \(\chi_{7605}(113, \cdot)\) n/a 52224 48
7605.2.hl \(\chi_{7605}(187, \cdot)\) n/a 52224 48
7605.2.hm \(\chi_{7605}(163, \cdot)\) n/a 21744 48
7605.2.hp \(\chi_{7605}(67, \cdot)\) n/a 52224 48
7605.2.hr \(\chi_{7605}(58, \cdot)\) n/a 52224 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7605))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7605)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(195))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(507))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(585))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(845))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1521))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2535))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7605))\)\(^{\oplus 1}\)