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Properties

Label 4290.2
Level 4290
Weight 2
Dimension 107743
Nonzero newspaces 80
Sturm bound 1935360

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Defining parameters

Level: \( N \) = \( 4290 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 80 \)
Sturm bound: \(1935360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4290))\).

Total New Old
Modular forms 491520 107743 383777
Cusp forms 476161 107743 368418
Eisenstein series 15359 0 15359

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4290))\)

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
4290.2.a \(\chi_{4290}(1, \cdot)\) 4290.2.a.a 1 1
4290.2.a.b 1
4290.2.a.c 1
4290.2.a.d 1
4290.2.a.e 1
4290.2.a.f 1
4290.2.a.g 1
4290.2.a.h 1
4290.2.a.i 1
4290.2.a.j 1
4290.2.a.k 1
4290.2.a.l 1
4290.2.a.m 1
4290.2.a.n 1
4290.2.a.o 1
4290.2.a.p 1
4290.2.a.q 1
4290.2.a.r 1
4290.2.a.s 1
4290.2.a.t 1
4290.2.a.u 1
4290.2.a.v 1
4290.2.a.w 1
4290.2.a.x 1
4290.2.a.y 1
4290.2.a.z 1
4290.2.a.ba 1
4290.2.a.bb 1
4290.2.a.bc 1
4290.2.a.bd 2
4290.2.a.be 2
4290.2.a.bf 2
4290.2.a.bg 2
4290.2.a.bh 2
4290.2.a.bi 2
4290.2.a.bj 2
4290.2.a.bk 2
4290.2.a.bl 3
4290.2.a.bm 3
4290.2.a.bn 3
4290.2.a.bo 3
4290.2.a.bp 3
4290.2.a.bq 3
4290.2.a.br 4
4290.2.a.bs 4
4290.2.a.bt 4
4290.2.a.bu 4
4290.2.d \(\chi_{4290}(859, \cdot)\) n/a 120 1
4290.2.e \(\chi_{4290}(4289, \cdot)\) n/a 336 1
4290.2.f \(\chi_{4290}(131, \cdot)\) n/a 192 1
4290.2.g \(\chi_{4290}(3301, \cdot)\) 4290.2.g.a 2 1
4290.2.g.b 2
4290.2.g.c 2
4290.2.g.d 2
4290.2.g.e 2
4290.2.g.f 2
4290.2.g.g 2
4290.2.g.h 2
4290.2.g.i 2
4290.2.g.j 2
4290.2.g.k 2
4290.2.g.l 2
4290.2.g.m 4
4290.2.g.n 4
4290.2.g.o 4
4290.2.g.p 6
4290.2.g.q 6
4290.2.g.r 8
4290.2.g.s 10
4290.2.g.t 10
4290.2.g.u 12
4290.2.j \(\chi_{4290}(4159, \cdot)\) n/a 144 1
4290.2.k \(\chi_{4290}(989, \cdot)\) n/a 288 1
4290.2.p \(\chi_{4290}(3431, \cdot)\) n/a 224 1
4290.2.q \(\chi_{4290}(991, \cdot)\) n/a 192 2
4290.2.r \(\chi_{4290}(463, \cdot)\) n/a 280 2
4290.2.s \(\chi_{4290}(1253, \cdot)\) n/a 672 2
4290.2.v \(\chi_{4290}(749, \cdot)\) n/a 560 2
4290.2.x \(\chi_{4290}(109, \cdot)\) n/a 336 2
4290.2.bb \(\chi_{4290}(2287, \cdot)\) n/a 336 2
4290.2.bc \(\chi_{4290}(287, \cdot)\) n/a 480 2
4290.2.bf \(\chi_{4290}(1013, \cdot)\) n/a 560 2
4290.2.bg \(\chi_{4290}(703, \cdot)\) n/a 288 2
4290.2.bh \(\chi_{4290}(2881, \cdot)\) n/a 224 2
4290.2.bj \(\chi_{4290}(551, \cdot)\) n/a 384 2
4290.2.bl \(\chi_{4290}(593, \cdot)\) n/a 672 2
4290.2.bm \(\chi_{4290}(1123, \cdot)\) n/a 280 2
4290.2.bp \(\chi_{4290}(1171, \cdot)\) n/a 384 4
4290.2.bq \(\chi_{4290}(2441, \cdot)\) n/a 448 2
4290.2.bv \(\chi_{4290}(659, \cdot)\) n/a 672 2
4290.2.bw \(\chi_{4290}(199, \cdot)\) n/a 288 2
4290.2.bz \(\chi_{4290}(2311, \cdot)\) n/a 192 2
4290.2.ca \(\chi_{4290}(1121, \cdot)\) n/a 448 2
4290.2.cb \(\chi_{4290}(329, \cdot)\) n/a 672 2
4290.2.cc \(\chi_{4290}(529, \cdot)\) n/a 272 2
4290.2.cf \(\chi_{4290}(701, \cdot)\) n/a 896 4
4290.2.ck \(\chi_{4290}(1039, \cdot)\) n/a 672 4
4290.2.cl \(\chi_{4290}(2549, \cdot)\) n/a 1152 4
4290.2.co \(\chi_{4290}(1691, \cdot)\) n/a 768 4
4290.2.cp \(\chi_{4290}(181, \cdot)\) n/a 448 4
4290.2.cq \(\chi_{4290}(2029, \cdot)\) n/a 576 4
4290.2.cr \(\chi_{4290}(1559, \cdot)\) n/a 1344 4
4290.2.cw \(\chi_{4290}(397, \cdot)\) n/a 560 4
4290.2.cx \(\chi_{4290}(197, \cdot)\) n/a 1344 4
4290.2.cz \(\chi_{4290}(1211, \cdot)\) n/a 736 4
4290.2.db \(\chi_{4290}(241, \cdot)\) n/a 448 4
4290.2.dc \(\chi_{4290}(23, \cdot)\) n/a 1120 4
4290.2.dd \(\chi_{4290}(373, \cdot)\) n/a 672 4
4290.2.dg \(\chi_{4290}(43, \cdot)\) n/a 672 4
4290.2.dh \(\chi_{4290}(1277, \cdot)\) n/a 1120 4
4290.2.dl \(\chi_{4290}(769, \cdot)\) n/a 672 4
4290.2.dn \(\chi_{4290}(89, \cdot)\) n/a 1120 4
4290.2.dq \(\chi_{4290}(527, \cdot)\) n/a 1344 4
4290.2.dr \(\chi_{4290}(67, \cdot)\) n/a 560 4
4290.2.ds \(\chi_{4290}(841, \cdot)\) n/a 896 8
4290.2.dv \(\chi_{4290}(697, \cdot)\) n/a 1344 8
4290.2.dw \(\chi_{4290}(1097, \cdot)\) n/a 2688 8
4290.2.dy \(\chi_{4290}(151, \cdot)\) n/a 896 8
4290.2.ea \(\chi_{4290}(1061, \cdot)\) n/a 1792 8
4290.2.eb \(\chi_{4290}(547, \cdot)\) n/a 1152 8
4290.2.ec \(\chi_{4290}(467, \cdot)\) n/a 2688 8
4290.2.ef \(\chi_{4290}(53, \cdot)\) n/a 2304 8
4290.2.eg \(\chi_{4290}(337, \cdot)\) n/a 1344 8
4290.2.ek \(\chi_{4290}(1919, \cdot)\) n/a 2688 8
4290.2.em \(\chi_{4290}(1009, \cdot)\) n/a 1344 8
4290.2.ep \(\chi_{4290}(83, \cdot)\) n/a 2688 8
4290.2.eq \(\chi_{4290}(577, \cdot)\) n/a 1344 8
4290.2.et \(\chi_{4290}(569, \cdot)\) n/a 2688 8
4290.2.eu \(\chi_{4290}(289, \cdot)\) n/a 1344 8
4290.2.ev \(\chi_{4290}(361, \cdot)\) n/a 896 8
4290.2.ew \(\chi_{4290}(1361, \cdot)\) n/a 1792 8
4290.2.ez \(\chi_{4290}(29, \cdot)\) n/a 2688 8
4290.2.fa \(\chi_{4290}(49, \cdot)\) n/a 1344 8
4290.2.ff \(\chi_{4290}(101, \cdot)\) n/a 1792 8
4290.2.fg \(\chi_{4290}(97, \cdot)\) n/a 2688 16
4290.2.fh \(\chi_{4290}(167, \cdot)\) n/a 5376 16
4290.2.fk \(\chi_{4290}(19, \cdot)\) n/a 2688 16
4290.2.fm \(\chi_{4290}(59, \cdot)\) n/a 5376 16
4290.2.fq \(\chi_{4290}(113, \cdot)\) n/a 5376 16
4290.2.fr \(\chi_{4290}(127, \cdot)\) n/a 2688 16
4290.2.fu \(\chi_{4290}(217, \cdot)\) n/a 2688 16
4290.2.fv \(\chi_{4290}(257, \cdot)\) n/a 5376 16
4290.2.fw \(\chi_{4290}(71, \cdot)\) n/a 3584 16
4290.2.fy \(\chi_{4290}(271, \cdot)\) n/a 1792 16
4290.2.ga \(\chi_{4290}(227, \cdot)\) n/a 5376 16
4290.2.gb \(\chi_{4290}(37, \cdot)\) n/a 2688 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4290))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4290)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(130))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(143))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(195))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(286))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(330))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(390))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(429))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(715))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(858))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1430))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2145))\)\(^{\oplus 2}\)