Properties

Label 5390.2
Level 5390
Weight 2
Dimension 244136
Nonzero newspaces 48
Sturm bound 3386880

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Defining parameters

Level: \( N \) = \( 5390 = 2 \cdot 5 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(3386880\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5390))\).

Total New Old
Modular forms 856320 244136 612184
Cusp forms 837121 244136 592985
Eisenstein series 19199 0 19199

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5390))\)

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
5390.2.a \(\chi_{5390}(1, \cdot)\) 5390.2.a.a 1 1
5390.2.a.b 1
5390.2.a.c 1
5390.2.a.d 1
5390.2.a.e 1
5390.2.a.f 1
5390.2.a.g 1
5390.2.a.h 1
5390.2.a.i 1
5390.2.a.j 1
5390.2.a.k 1
5390.2.a.l 1
5390.2.a.m 1
5390.2.a.n 1
5390.2.a.o 1
5390.2.a.p 1
5390.2.a.q 1
5390.2.a.r 1
5390.2.a.s 1
5390.2.a.t 1
5390.2.a.u 1
5390.2.a.v 1
5390.2.a.w 1
5390.2.a.x 1
5390.2.a.y 1
5390.2.a.z 1
5390.2.a.ba 1
5390.2.a.bb 1
5390.2.a.bc 1
5390.2.a.bd 1
5390.2.a.be 1
5390.2.a.bf 1
5390.2.a.bg 1
5390.2.a.bh 1
5390.2.a.bi 1
5390.2.a.bj 1
5390.2.a.bk 2
5390.2.a.bl 2
5390.2.a.bm 2
5390.2.a.bn 2
5390.2.a.bo 2
5390.2.a.bp 2
5390.2.a.bq 2
5390.2.a.br 2
5390.2.a.bs 2
5390.2.a.bt 2
5390.2.a.bu 2
5390.2.a.bv 3
5390.2.a.bw 3
5390.2.a.bx 3
5390.2.a.by 3
5390.2.a.bz 3
5390.2.a.ca 3
5390.2.a.cb 4
5390.2.a.cc 4
5390.2.a.cd 4
5390.2.a.ce 4
5390.2.a.cf 4
5390.2.a.cg 4
5390.2.a.ch 5
5390.2.a.ci 5
5390.2.a.cj 6
5390.2.a.ck 6
5390.2.a.cl 6
5390.2.a.cm 6
5390.2.c \(\chi_{5390}(1079, \cdot)\) n/a 206 1
5390.2.e \(\chi_{5390}(4311, \cdot)\) n/a 160 1
5390.2.g \(\chi_{5390}(5389, \cdot)\) n/a 240 1
5390.2.i \(\chi_{5390}(3301, \cdot)\) n/a 272 2
5390.2.l \(\chi_{5390}(3037, \cdot)\) n/a 400 2
5390.2.m \(\chi_{5390}(197, \cdot)\) n/a 492 2
5390.2.n \(\chi_{5390}(1961, \cdot)\) n/a 656 4
5390.2.o \(\chi_{5390}(1979, \cdot)\) n/a 480 2
5390.2.r \(\chi_{5390}(4379, \cdot)\) n/a 400 2
5390.2.t \(\chi_{5390}(901, \cdot)\) n/a 320 2
5390.2.v \(\chi_{5390}(771, \cdot)\) n/a 1152 6
5390.2.x \(\chi_{5390}(1469, \cdot)\) n/a 960 4
5390.2.z \(\chi_{5390}(391, \cdot)\) n/a 640 4
5390.2.bb \(\chi_{5390}(3039, \cdot)\) n/a 984 4
5390.2.bd \(\chi_{5390}(1783, \cdot)\) n/a 800 4
5390.2.be \(\chi_{5390}(263, \cdot)\) n/a 960 4
5390.2.bj \(\chi_{5390}(769, \cdot)\) n/a 2016 6
5390.2.bl \(\chi_{5390}(461, \cdot)\) n/a 1344 6
5390.2.bn \(\chi_{5390}(309, \cdot)\) n/a 1680 6
5390.2.bo \(\chi_{5390}(361, \cdot)\) n/a 1280 8
5390.2.bp \(\chi_{5390}(393, \cdot)\) n/a 1968 8
5390.2.bq \(\chi_{5390}(97, \cdot)\) n/a 1920 8
5390.2.bt \(\chi_{5390}(221, \cdot)\) n/a 2208 12
5390.2.bw \(\chi_{5390}(43, \cdot)\) n/a 4032 12
5390.2.bx \(\chi_{5390}(573, \cdot)\) n/a 3360 12
5390.2.bz \(\chi_{5390}(2371, \cdot)\) n/a 1280 8
5390.2.cb \(\chi_{5390}(949, \cdot)\) n/a 1920 8
5390.2.ce \(\chi_{5390}(19, \cdot)\) n/a 1920 8
5390.2.cf \(\chi_{5390}(71, \cdot)\) n/a 5376 24
5390.2.cg \(\chi_{5390}(131, \cdot)\) n/a 2688 12
5390.2.ci \(\chi_{5390}(529, \cdot)\) n/a 3360 12
5390.2.cl \(\chi_{5390}(439, \cdot)\) n/a 4032 12
5390.2.cp \(\chi_{5390}(557, \cdot)\) n/a 3840 16
5390.2.cq \(\chi_{5390}(313, \cdot)\) n/a 3840 16
5390.2.cr \(\chi_{5390}(169, \cdot)\) n/a 8064 24
5390.2.ct \(\chi_{5390}(41, \cdot)\) n/a 5376 24
5390.2.cv \(\chi_{5390}(139, \cdot)\) n/a 8064 24
5390.2.cy \(\chi_{5390}(417, \cdot)\) n/a 8064 24
5390.2.cz \(\chi_{5390}(243, \cdot)\) n/a 6720 24
5390.2.dc \(\chi_{5390}(81, \cdot)\) n/a 10752 48
5390.2.dd \(\chi_{5390}(27, \cdot)\) n/a 16128 48
5390.2.de \(\chi_{5390}(57, \cdot)\) n/a 16128 48
5390.2.di \(\chi_{5390}(299, \cdot)\) n/a 16128 48
5390.2.dl \(\chi_{5390}(9, \cdot)\) n/a 16128 48
5390.2.dn \(\chi_{5390}(61, \cdot)\) n/a 10752 48
5390.2.dq \(\chi_{5390}(3, \cdot)\) n/a 32256 96
5390.2.dr \(\chi_{5390}(107, \cdot)\) n/a 32256 96

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5390))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5390)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(385))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(490))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(539))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(770))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1078))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2695))\)\(^{\oplus 2}\)