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Properties

Label 4640.2
Level 4640
Weight 2
Dimension 330228
Nonzero newspaces 72
Sturm bound 2580480

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Defining parameters

Level: \( N \) = \( 4640 = 2^{5} \cdot 5 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 72 \)
Sturm bound: \(2580480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4640))\).

Total New Old
Modular forms 652288 333468 318820
Cusp forms 637953 330228 307725
Eisenstein series 14335 3240 11095

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4640))\)

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
4640.2.a \(\chi_{4640}(1, \cdot)\) 4640.2.a.a 1 1
4640.2.a.b 1
4640.2.a.c 1
4640.2.a.d 1
4640.2.a.e 1
4640.2.a.f 1
4640.2.a.g 2
4640.2.a.h 2
4640.2.a.i 2
4640.2.a.j 3
4640.2.a.k 3
4640.2.a.l 4
4640.2.a.m 4
4640.2.a.n 4
4640.2.a.o 4
4640.2.a.p 4
4640.2.a.q 4
4640.2.a.r 4
4640.2.a.s 6
4640.2.a.t 6
4640.2.a.u 6
4640.2.a.v 6
4640.2.a.w 7
4640.2.a.x 7
4640.2.a.y 8
4640.2.a.z 10
4640.2.a.ba 10
4640.2.d \(\chi_{4640}(929, \cdot)\) n/a 168 1
4640.2.e \(\chi_{4640}(2609, \cdot)\) n/a 176 1
4640.2.f \(\chi_{4640}(2321, \cdot)\) n/a 112 1
4640.2.g \(\chi_{4640}(4001, \cdot)\) n/a 120 1
4640.2.j \(\chi_{4640}(289, \cdot)\) n/a 180 1
4640.2.k \(\chi_{4640}(3249, \cdot)\) n/a 168 1
4640.2.p \(\chi_{4640}(1681, \cdot)\) n/a 120 1
4640.2.q \(\chi_{4640}(2279, \cdot)\) None 0 2
4640.2.t \(\chi_{4640}(1623, \cdot)\) None 0 2
4640.2.u \(\chi_{4640}(1873, \cdot)\) n/a 352 2
4640.2.w \(\chi_{4640}(2337, \cdot)\) n/a 360 2
4640.2.z \(\chi_{4640}(407, \cdot)\) None 0 2
4640.2.bb \(\chi_{4640}(3671, \cdot)\) None 0 2
4640.2.bc \(\chi_{4640}(191, \cdot)\) n/a 240 2
4640.2.bf \(\chi_{4640}(521, \cdot)\) None 0 2
4640.2.bh \(\chi_{4640}(1161, \cdot)\) None 0 2
4640.2.bi \(\chi_{4640}(911, \cdot)\) n/a 240 2
4640.2.bl \(\chi_{4640}(1433, \cdot)\) None 0 2
4640.2.bo \(\chi_{4640}(1567, \cdot)\) n/a 336 2
4640.2.bp \(\chi_{4640}(463, \cdot)\) n/a 352 2
4640.2.bq \(\chi_{4640}(713, \cdot)\) None 0 2
4640.2.bs \(\chi_{4640}(1897, \cdot)\) None 0 2
4640.2.bu \(\chi_{4640}(1103, \cdot)\) n/a 336 2
4640.2.bv \(\chi_{4640}(927, \cdot)\) n/a 360 2
4640.2.bz \(\chi_{4640}(1177, \cdot)\) None 0 2
4640.2.cb \(\chi_{4640}(1839, \cdot)\) n/a 352 2
4640.2.cc \(\chi_{4640}(2089, \cdot)\) None 0 2
4640.2.ce \(\chi_{4640}(1449, \cdot)\) None 0 2
4640.2.ch \(\chi_{4640}(1119, \cdot)\) n/a 360 2
4640.2.cj \(\chi_{4640}(679, \cdot)\) None 0 2
4640.2.ck \(\chi_{4640}(2263, \cdot)\) None 0 2
4640.2.cn \(\chi_{4640}(737, \cdot)\) n/a 360 2
4640.2.cp \(\chi_{4640}(17, \cdot)\) n/a 352 2
4640.2.cq \(\chi_{4640}(3943, \cdot)\) None 0 2
4640.2.cs \(\chi_{4640}(1351, \cdot)\) None 0 2
4640.2.cu \(\chi_{4640}(161, \cdot)\) n/a 720 6
4640.2.cw \(\chi_{4640}(597, \cdot)\) n/a 2864 4
4640.2.cy \(\chi_{4640}(523, \cdot)\) n/a 2688 4
4640.2.da \(\chi_{4640}(1507, \cdot)\) n/a 2864 4
4640.2.db \(\chi_{4640}(1293, \cdot)\) n/a 2864 4
4640.2.dd \(\chi_{4640}(869, \cdot)\) n/a 2864 4
4640.2.dg \(\chi_{4640}(581, \cdot)\) n/a 1792 4
4640.2.dh \(\chi_{4640}(331, \cdot)\) n/a 1920 4
4640.2.dk \(\chi_{4640}(1491, \cdot)\) n/a 1920 4
4640.2.dl \(\chi_{4640}(1259, \cdot)\) n/a 2864 4
4640.2.do \(\chi_{4640}(99, \cdot)\) n/a 2864 4
4640.2.dq \(\chi_{4640}(1101, \cdot)\) n/a 1920 4
4640.2.dr \(\chi_{4640}(349, \cdot)\) n/a 2688 4
4640.2.dt \(\chi_{4640}(853, \cdot)\) n/a 2864 4
4640.2.dv \(\chi_{4640}(987, \cdot)\) n/a 2688 4
4640.2.dx \(\chi_{4640}(347, \cdot)\) n/a 2864 4
4640.2.ea \(\chi_{4640}(133, \cdot)\) n/a 2864 4
4640.2.eb \(\chi_{4640}(241, \cdot)\) n/a 720 6
4640.2.eg \(\chi_{4640}(49, \cdot)\) n/a 1056 6
4640.2.eh \(\chi_{4640}(129, \cdot)\) n/a 1080 6
4640.2.ek \(\chi_{4640}(961, \cdot)\) n/a 720 6
4640.2.el \(\chi_{4640}(81, \cdot)\) n/a 720 6
4640.2.em \(\chi_{4640}(209, \cdot)\) n/a 1056 6
4640.2.en \(\chi_{4640}(1089, \cdot)\) n/a 1080 6
4640.2.er \(\chi_{4640}(391, \cdot)\) None 0 12
4640.2.et \(\chi_{4640}(903, \cdot)\) None 0 12
4640.2.eu \(\chi_{4640}(97, \cdot)\) n/a 2160 12
4640.2.ew \(\chi_{4640}(113, \cdot)\) n/a 2112 12
4640.2.ez \(\chi_{4640}(7, \cdot)\) None 0 12
4640.2.fa \(\chi_{4640}(39, \cdot)\) None 0 12
4640.2.fc \(\chi_{4640}(159, \cdot)\) n/a 2160 12
4640.2.ff \(\chi_{4640}(169, \cdot)\) None 0 12
4640.2.fh \(\chi_{4640}(9, \cdot)\) None 0 12
4640.2.fi \(\chi_{4640}(79, \cdot)\) n/a 2112 12
4640.2.fl \(\chi_{4640}(73, \cdot)\) None 0 12
4640.2.fo \(\chi_{4640}(63, \cdot)\) n/a 2160 12
4640.2.fp \(\chi_{4640}(687, \cdot)\) n/a 2112 12
4640.2.fq \(\chi_{4640}(617, \cdot)\) None 0 12
4640.2.fs \(\chi_{4640}(537, \cdot)\) None 0 12
4640.2.fu \(\chi_{4640}(207, \cdot)\) n/a 2112 12
4640.2.fv \(\chi_{4640}(223, \cdot)\) n/a 2160 12
4640.2.fz \(\chi_{4640}(137, \cdot)\) None 0 12
4640.2.gb \(\chi_{4640}(271, \cdot)\) n/a 1440 12
4640.2.gc \(\chi_{4640}(121, \cdot)\) None 0 12
4640.2.ge \(\chi_{4640}(281, \cdot)\) None 0 12
4640.2.gh \(\chi_{4640}(31, \cdot)\) n/a 1440 12
4640.2.gi \(\chi_{4640}(311, \cdot)\) None 0 12
4640.2.gk \(\chi_{4640}(103, \cdot)\) None 0 12
4640.2.gn \(\chi_{4640}(337, \cdot)\) n/a 2112 12
4640.2.gp \(\chi_{4640}(417, \cdot)\) n/a 2160 12
4640.2.gq \(\chi_{4640}(167, \cdot)\) None 0 12
4640.2.gt \(\chi_{4640}(279, \cdot)\) None 0 12
4640.2.gu \(\chi_{4640}(77, \cdot)\) n/a 17184 24
4640.2.gw \(\chi_{4640}(187, \cdot)\) n/a 17184 24
4640.2.gy \(\chi_{4640}(83, \cdot)\) n/a 17184 24
4640.2.hb \(\chi_{4640}(293, \cdot)\) n/a 17184 24
4640.2.hc \(\chi_{4640}(141, \cdot)\) n/a 11520 24
4640.2.hf \(\chi_{4640}(109, \cdot)\) n/a 17184 24
4640.2.hh \(\chi_{4640}(259, \cdot)\) n/a 17184 24
4640.2.hi \(\chi_{4640}(19, \cdot)\) n/a 17184 24
4640.2.hl \(\chi_{4640}(11, \cdot)\) n/a 11520 24
4640.2.hm \(\chi_{4640}(171, \cdot)\) n/a 11520 24
4640.2.hp \(\chi_{4640}(429, \cdot)\) n/a 17184 24
4640.2.hq \(\chi_{4640}(341, \cdot)\) n/a 11520 24
4640.2.ht \(\chi_{4640}(437, \cdot)\) n/a 17184 24
4640.2.hv \(\chi_{4640}(67, \cdot)\) n/a 17184 24
4640.2.hx \(\chi_{4640}(123, \cdot)\) n/a 17184 24
4640.2.hy \(\chi_{4640}(37, \cdot)\) n/a 17184 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4640))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4640)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(145))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(232))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(290))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(464))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(580))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(928))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1160))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2320))\)\(^{\oplus 2}\)