Properties

Label 4592.2
Level 4592
Weight 2
Dimension 345590
Nonzero newspaces 80
Sturm bound 2580480

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Defining parameters

Level: \( N \) = \( 4592 = 2^{4} \cdot 7 \cdot 41 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 80 \)
Sturm bound: \(2580480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4592))\).

Total New Old
Modular forms 651840 349102 302738
Cusp forms 638401 345590 292811
Eisenstein series 13439 3512 9927

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4592))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
4592.2.a \(\chi_{4592}(1, \cdot)\) 4592.2.a.a 1 1
4592.2.a.b 1
4592.2.a.c 1
4592.2.a.d 1
4592.2.a.e 1
4592.2.a.f 1
4592.2.a.g 1
4592.2.a.h 1
4592.2.a.i 1
4592.2.a.j 1
4592.2.a.k 1
4592.2.a.l 1
4592.2.a.m 2
4592.2.a.n 2
4592.2.a.o 2
4592.2.a.p 2
4592.2.a.q 2
4592.2.a.r 3
4592.2.a.s 3
4592.2.a.t 3
4592.2.a.u 3
4592.2.a.v 3
4592.2.a.w 3
4592.2.a.x 4
4592.2.a.y 4
4592.2.a.z 4
4592.2.a.ba 4
4592.2.a.bb 5
4592.2.a.bc 5
4592.2.a.bd 5
4592.2.a.be 5
4592.2.a.bf 6
4592.2.a.bg 6
4592.2.a.bh 7
4592.2.a.bi 8
4592.2.a.bj 8
4592.2.a.bk 9
4592.2.b \(\chi_{4592}(2297, \cdot)\) None 0 1
4592.2.e \(\chi_{4592}(4591, \cdot)\) n/a 168 1
4592.2.f \(\chi_{4592}(3361, \cdot)\) n/a 126 1
4592.2.i \(\chi_{4592}(3527, \cdot)\) None 0 1
4592.2.j \(\chi_{4592}(1231, \cdot)\) n/a 160 1
4592.2.m \(\chi_{4592}(1065, \cdot)\) None 0 1
4592.2.n \(\chi_{4592}(2295, \cdot)\) None 0 1
4592.2.q \(\chi_{4592}(1313, \cdot)\) n/a 320 2
4592.2.s \(\chi_{4592}(419, \cdot)\) n/a 1336 2
4592.2.t \(\chi_{4592}(1485, \cdot)\) n/a 1008 2
4592.2.w \(\chi_{4592}(1959, \cdot)\) None 0 2
4592.2.y \(\chi_{4592}(337, \cdot)\) n/a 252 2
4592.2.z \(\chi_{4592}(2213, \cdot)\) n/a 1008 2
4592.2.ba \(\chi_{4592}(83, \cdot)\) n/a 1280 2
4592.2.bf \(\chi_{4592}(1149, \cdot)\) n/a 960 2
4592.2.bg \(\chi_{4592}(1147, \cdot)\) n/a 1336 2
4592.2.bi \(\chi_{4592}(1567, \cdot)\) n/a 336 2
4592.2.bk \(\chi_{4592}(729, \cdot)\) None 0 2
4592.2.bm \(\chi_{4592}(3781, \cdot)\) n/a 1008 2
4592.2.bn \(\chi_{4592}(2715, \cdot)\) n/a 1336 2
4592.2.bp \(\chi_{4592}(2353, \cdot)\) n/a 504 4
4592.2.br \(\chi_{4592}(327, \cdot)\) None 0 2
4592.2.bu \(\chi_{4592}(2377, \cdot)\) None 0 2
4592.2.bv \(\chi_{4592}(3855, \cdot)\) n/a 320 2
4592.2.by \(\chi_{4592}(1559, \cdot)\) None 0 2
4592.2.bz \(\chi_{4592}(81, \cdot)\) n/a 332 2
4592.2.cc \(\chi_{4592}(2623, \cdot)\) n/a 336 2
4592.2.cd \(\chi_{4592}(3609, \cdot)\) None 0 2
4592.2.cg \(\chi_{4592}(547, \cdot)\) n/a 2016 4
4592.2.ci \(\chi_{4592}(629, \cdot)\) n/a 2672 4
4592.2.cl \(\chi_{4592}(489, \cdot)\) None 0 4
4592.2.cm \(\chi_{4592}(1777, \cdot)\) n/a 664 4
4592.2.cp \(\chi_{4592}(407, \cdot)\) None 0 4
4592.2.cq \(\chi_{4592}(1695, \cdot)\) n/a 504 4
4592.2.cs \(\chi_{4592}(659, \cdot)\) n/a 2016 4
4592.2.cu \(\chi_{4592}(741, \cdot)\) n/a 2672 4
4592.2.cv \(\chi_{4592}(1287, \cdot)\) None 0 4
4592.2.cy \(\chi_{4592}(113, \cdot)\) n/a 504 4
4592.2.cz \(\chi_{4592}(783, \cdot)\) n/a 672 4
4592.2.dc \(\chi_{4592}(57, \cdot)\) None 0 4
4592.2.df \(\chi_{4592}(3079, \cdot)\) None 0 4
4592.2.dg \(\chi_{4592}(1849, \cdot)\) None 0 4
4592.2.dj \(\chi_{4592}(223, \cdot)\) n/a 672 4
4592.2.dk \(\chi_{4592}(747, \cdot)\) n/a 2672 4
4592.2.dn \(\chi_{4592}(501, \cdot)\) n/a 2672 4
4592.2.do \(\chi_{4592}(9, \cdot)\) None 0 4
4592.2.dq \(\chi_{4592}(255, \cdot)\) n/a 672 4
4592.2.du \(\chi_{4592}(411, \cdot)\) n/a 2560 4
4592.2.dv \(\chi_{4592}(1229, \cdot)\) n/a 2672 4
4592.2.dw \(\chi_{4592}(1475, \cdot)\) n/a 2672 4
4592.2.dx \(\chi_{4592}(165, \cdot)\) n/a 2560 4
4592.2.ea \(\chi_{4592}(401, \cdot)\) n/a 664 4
4592.2.ec \(\chi_{4592}(647, \cdot)\) None 0 4
4592.2.ee \(\chi_{4592}(2797, \cdot)\) n/a 2672 4
4592.2.eh \(\chi_{4592}(3043, \cdot)\) n/a 2672 4
4592.2.ei \(\chi_{4592}(305, \cdot)\) n/a 1328 8
4592.2.ek \(\chi_{4592}(197, \cdot)\) n/a 4032 8
4592.2.el \(\chi_{4592}(531, \cdot)\) n/a 5344 8
4592.2.en \(\chi_{4592}(169, \cdot)\) None 0 8
4592.2.ep \(\chi_{4592}(1455, \cdot)\) n/a 1344 8
4592.2.er \(\chi_{4592}(195, \cdot)\) n/a 5344 8
4592.2.es \(\chi_{4592}(141, \cdot)\) n/a 4032 8
4592.2.ex \(\chi_{4592}(139, \cdot)\) n/a 5344 8
4592.2.ey \(\chi_{4592}(701, \cdot)\) n/a 4032 8
4592.2.ez \(\chi_{4592}(225, \cdot)\) n/a 1008 8
4592.2.fb \(\chi_{4592}(279, \cdot)\) None 0 8
4592.2.fe \(\chi_{4592}(251, \cdot)\) n/a 5344 8
4592.2.ff \(\chi_{4592}(869, \cdot)\) n/a 4032 8
4592.2.fh \(\chi_{4592}(325, \cdot)\) n/a 5344 8
4592.2.fj \(\chi_{4592}(219, \cdot)\) n/a 5344 8
4592.2.fl \(\chi_{4592}(79, \cdot)\) n/a 1344 8
4592.2.fm \(\chi_{4592}(711, \cdot)\) None 0 8
4592.2.fp \(\chi_{4592}(465, \cdot)\) n/a 1328 8
4592.2.fq \(\chi_{4592}(2105, \cdot)\) None 0 8
4592.2.ft \(\chi_{4592}(437, \cdot)\) n/a 5344 8
4592.2.fv \(\chi_{4592}(331, \cdot)\) n/a 5344 8
4592.2.fy \(\chi_{4592}(1615, \cdot)\) n/a 1344 8
4592.2.fz \(\chi_{4592}(25, \cdot)\) None 0 8
4592.2.gc \(\chi_{4592}(1111, \cdot)\) None 0 8
4592.2.gf \(\chi_{4592}(1369, \cdot)\) None 0 8
4592.2.gg \(\chi_{4592}(31, \cdot)\) n/a 1344 8
4592.2.gj \(\chi_{4592}(865, \cdot)\) n/a 1328 8
4592.2.gk \(\chi_{4592}(215, \cdot)\) None 0 8
4592.2.gm \(\chi_{4592}(69, \cdot)\) n/a 10688 16
4592.2.go \(\chi_{4592}(995, \cdot)\) n/a 8064 16
4592.2.gq \(\chi_{4592}(15, \cdot)\) n/a 2016 16
4592.2.gr \(\chi_{4592}(71, \cdot)\) None 0 16
4592.2.gu \(\chi_{4592}(97, \cdot)\) n/a 2656 16
4592.2.gv \(\chi_{4592}(153, \cdot)\) None 0 16
4592.2.gy \(\chi_{4592}(13, \cdot)\) n/a 10688 16
4592.2.ha \(\chi_{4592}(99, \cdot)\) n/a 8064 16
4592.2.hc \(\chi_{4592}(613, \cdot)\) n/a 10688 16
4592.2.hf \(\chi_{4592}(115, \cdot)\) n/a 10688 16
4592.2.hh \(\chi_{4592}(87, \cdot)\) None 0 16
4592.2.hj \(\chi_{4592}(289, \cdot)\) n/a 2656 16
4592.2.hm \(\chi_{4592}(37, \cdot)\) n/a 10688 16
4592.2.hn \(\chi_{4592}(187, \cdot)\) n/a 10688 16
4592.2.ho \(\chi_{4592}(277, \cdot)\) n/a 10688 16
4592.2.hp \(\chi_{4592}(59, \cdot)\) n/a 10688 16
4592.2.ht \(\chi_{4592}(143, \cdot)\) n/a 2688 16
4592.2.hv \(\chi_{4592}(121, \cdot)\) None 0 16
4592.2.hw \(\chi_{4592}(131, \cdot)\) n/a 10688 16
4592.2.hz \(\chi_{4592}(333, \cdot)\) n/a 10688 16
4592.2.ib \(\chi_{4592}(11, \cdot)\) n/a 21376 32
4592.2.id \(\chi_{4592}(101, \cdot)\) n/a 21376 32
4592.2.ig \(\chi_{4592}(89, \cdot)\) None 0 32
4592.2.ih \(\chi_{4592}(17, \cdot)\) n/a 5312 32
4592.2.ik \(\chi_{4592}(135, \cdot)\) None 0 32
4592.2.il \(\chi_{4592}(95, \cdot)\) n/a 5376 32
4592.2.in \(\chi_{4592}(275, \cdot)\) n/a 21376 32
4592.2.ip \(\chi_{4592}(341, \cdot)\) n/a 21376 32

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4592))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4592)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(82))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(164))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(287))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(328))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(574))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(656))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1148))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2296))\)\(^{\oplus 2}\)