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Properties

Label 4655.2
Level 4655
Weight 2
Dimension 735722
Nonzero newspaces 96
Sturm bound 3386880

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Defining parameters

Level: \( N \) = \( 4655 = 5 \cdot 7^{2} \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 96 \)
Sturm bound: \(3386880\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4655))\).

Total New Old
Modular forms 855360 745618 109742
Cusp forms 838081 735722 102359
Eisenstein series 17279 9896 7383

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4655))\)

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
4655.2.a \(\chi_{4655}(1, \cdot)\) 4655.2.a.a 1 1
4655.2.a.b 1
4655.2.a.c 1
4655.2.a.d 1
4655.2.a.e 1
4655.2.a.f 1
4655.2.a.g 1
4655.2.a.h 1
4655.2.a.i 1
4655.2.a.j 1
4655.2.a.k 1
4655.2.a.l 1
4655.2.a.m 1
4655.2.a.n 1
4655.2.a.o 1
4655.2.a.p 1
4655.2.a.q 1
4655.2.a.r 1
4655.2.a.s 1
4655.2.a.t 2
4655.2.a.u 3
4655.2.a.v 3
4655.2.a.w 3
4655.2.a.x 3
4655.2.a.y 4
4655.2.a.z 4
4655.2.a.ba 4
4655.2.a.bb 4
4655.2.a.bc 6
4655.2.a.bd 7
4655.2.a.be 8
4655.2.a.bf 8
4655.2.a.bg 8
4655.2.a.bh 8
4655.2.a.bi 8
4655.2.a.bj 10
4655.2.a.bk 10
4655.2.a.bl 11
4655.2.a.bm 11
4655.2.a.bn 12
4655.2.a.bo 12
4655.2.a.bp 13
4655.2.a.bq 13
4655.2.a.br 26
4655.2.a.bs 26
4655.2.b \(\chi_{4655}(2794, \cdot)\) n/a 368 1
4655.2.d \(\chi_{4655}(1861, \cdot)\) n/a 264 1
4655.2.g \(\chi_{4655}(4654, \cdot)\) n/a 392 1
4655.2.i \(\chi_{4655}(3431, \cdot)\) n/a 544 2
4655.2.j \(\chi_{4655}(2186, \cdot)\) n/a 480 2
4655.2.k \(\chi_{4655}(961, \cdot)\) n/a 536 2
4655.2.l \(\chi_{4655}(1341, \cdot)\) n/a 536 2
4655.2.m \(\chi_{4655}(2547, \cdot)\) n/a 720 2
4655.2.p \(\chi_{4655}(1177, \cdot)\) n/a 800 2
4655.2.r \(\chi_{4655}(411, \cdot)\) n/a 536 2
4655.2.t \(\chi_{4655}(4134, \cdot)\) n/a 784 2
4655.2.v \(\chi_{4655}(2824, \cdot)\) n/a 784 2
4655.2.y \(\chi_{4655}(2089, \cdot)\) n/a 784 2
4655.2.ba \(\chi_{4655}(734, \cdot)\) n/a 784 2
4655.2.bd \(\chi_{4655}(3754, \cdot)\) n/a 784 2
4655.2.bg \(\chi_{4655}(3951, \cdot)\) n/a 536 2
4655.2.bi \(\chi_{4655}(2596, \cdot)\) n/a 528 2
4655.2.bk \(\chi_{4655}(1569, \cdot)\) n/a 800 2
4655.2.bm \(\chi_{4655}(324, \cdot)\) n/a 720 2
4655.2.bn \(\chi_{4655}(31, \cdot)\) n/a 536 2
4655.2.bq \(\chi_{4655}(3204, \cdot)\) n/a 784 2
4655.2.bs \(\chi_{4655}(666, \cdot)\) n/a 2016 6
4655.2.bt \(\chi_{4655}(606, \cdot)\) n/a 1596 6
4655.2.bu \(\chi_{4655}(491, \cdot)\) n/a 1644 6
4655.2.bv \(\chi_{4655}(226, \cdot)\) n/a 1596 6
4655.2.bw \(\chi_{4655}(312, \cdot)\) n/a 1568 4
4655.2.bz \(\chi_{4655}(558, \cdot)\) n/a 1568 4
4655.2.ca \(\chi_{4655}(362, \cdot)\) n/a 1440 4
4655.2.cc \(\chi_{4655}(753, \cdot)\) n/a 1568 4
4655.2.ce \(\chi_{4655}(1912, \cdot)\) n/a 1600 4
4655.2.ch \(\chi_{4655}(68, \cdot)\) n/a 1568 4
4655.2.cj \(\chi_{4655}(1322, \cdot)\) n/a 1568 4
4655.2.cl \(\chi_{4655}(18, \cdot)\) n/a 1568 4
4655.2.cn \(\chi_{4655}(664, \cdot)\) n/a 3336 6
4655.2.cq \(\chi_{4655}(531, \cdot)\) n/a 2256 6
4655.2.cs \(\chi_{4655}(134, \cdot)\) n/a 3024 6
4655.2.cw \(\chi_{4655}(509, \cdot)\) n/a 2352 6
4655.2.cx \(\chi_{4655}(489, \cdot)\) n/a 2352 6
4655.2.cz \(\chi_{4655}(129, \cdot)\) n/a 2352 6
4655.2.dc \(\chi_{4655}(146, \cdot)\) n/a 1608 6
4655.2.df \(\chi_{4655}(656, \cdot)\) n/a 1596 6
4655.2.dg \(\chi_{4655}(99, \cdot)\) n/a 2400 6
4655.2.dj \(\chi_{4655}(214, \cdot)\) n/a 2352 6
4655.2.dk \(\chi_{4655}(814, \cdot)\) n/a 2352 6
4655.2.dm \(\chi_{4655}(166, \cdot)\) n/a 1596 6
4655.2.do \(\chi_{4655}(11, \cdot)\) n/a 4464 12
4655.2.dp \(\chi_{4655}(296, \cdot)\) n/a 4464 12
4655.2.dq \(\chi_{4655}(191, \cdot)\) n/a 4032 12
4655.2.dr \(\chi_{4655}(106, \cdot)\) n/a 4512 12
4655.2.ds \(\chi_{4655}(113, \cdot)\) n/a 6672 12
4655.2.dv \(\chi_{4655}(153, \cdot)\) n/a 6048 12
4655.2.dw \(\chi_{4655}(508, \cdot)\) n/a 4704 12
4655.2.dy \(\chi_{4655}(148, \cdot)\) n/a 4800 12
4655.2.ea \(\chi_{4655}(313, \cdot)\) n/a 4704 12
4655.2.ec \(\chi_{4655}(538, \cdot)\) n/a 4704 12
4655.2.ef \(\chi_{4655}(803, \cdot)\) n/a 4704 12
4655.2.eh \(\chi_{4655}(67, \cdot)\) n/a 4704 12
4655.2.ej \(\chi_{4655}(544, \cdot)\) n/a 6672 12
4655.2.em \(\chi_{4655}(236, \cdot)\) n/a 4464 12
4655.2.en \(\chi_{4655}(39, \cdot)\) n/a 6048 12
4655.2.ep \(\chi_{4655}(64, \cdot)\) n/a 6672 12
4655.2.er \(\chi_{4655}(426, \cdot)\) n/a 4512 12
4655.2.et \(\chi_{4655}(341, \cdot)\) n/a 4464 12
4655.2.ew \(\chi_{4655}(429, \cdot)\) n/a 6672 12
4655.2.ez \(\chi_{4655}(69, \cdot)\) n/a 6672 12
4655.2.fb \(\chi_{4655}(94, \cdot)\) n/a 6672 12
4655.2.fe \(\chi_{4655}(164, \cdot)\) n/a 6672 12
4655.2.fg \(\chi_{4655}(144, \cdot)\) n/a 6672 12
4655.2.fi \(\chi_{4655}(1076, \cdot)\) n/a 4464 12
4655.2.fk \(\chi_{4655}(16, \cdot)\) n/a 13464 36
4655.2.fl \(\chi_{4655}(81, \cdot)\) n/a 13464 36
4655.2.fm \(\chi_{4655}(36, \cdot)\) n/a 13392 36
4655.2.fn \(\chi_{4655}(37, \cdot)\) n/a 13344 24
4655.2.fp \(\chi_{4655}(83, \cdot)\) n/a 13344 24
4655.2.fr \(\chi_{4655}(467, \cdot)\) n/a 13344 24
4655.2.fu \(\chi_{4655}(8, \cdot)\) n/a 13344 24
4655.2.fw \(\chi_{4655}(88, \cdot)\) n/a 13344 24
4655.2.fy \(\chi_{4655}(248, \cdot)\) n/a 12096 24
4655.2.fz \(\chi_{4655}(87, \cdot)\) n/a 13344 24
4655.2.gc \(\chi_{4655}(107, \cdot)\) n/a 13344 24
4655.2.gd \(\chi_{4655}(241, \cdot)\) n/a 13464 36
4655.2.gf \(\chi_{4655}(4, \cdot)\) n/a 20016 36
4655.2.gh \(\chi_{4655}(169, \cdot)\) n/a 20016 36
4655.2.gk \(\chi_{4655}(9, \cdot)\) n/a 20016 36
4655.2.gl \(\chi_{4655}(41, \cdot)\) n/a 13392 36
4655.2.go \(\chi_{4655}(136, \cdot)\) n/a 13464 36
4655.2.gq \(\chi_{4655}(299, \cdot)\) n/a 20016 36
4655.2.gt \(\chi_{4655}(59, \cdot)\) n/a 20016 36
4655.2.gu \(\chi_{4655}(34, \cdot)\) n/a 20016 36
4655.2.gz \(\chi_{4655}(2, \cdot)\) n/a 40032 72
4655.2.hb \(\chi_{4655}(138, \cdot)\) n/a 40032 72
4655.2.hc \(\chi_{4655}(17, \cdot)\) n/a 40032 72
4655.2.he \(\chi_{4655}(62, \cdot)\) n/a 40032 72
4655.2.hg \(\chi_{4655}(72, \cdot)\) n/a 40032 72
4655.2.hi \(\chi_{4655}(22, \cdot)\) n/a 40032 72

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4655))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4655)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(133))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(665))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(931))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4655))\)\(^{\oplus 1}\)