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Properties

Label 8450.2
Level 8450
Weight 2
Dimension 646481
Nonzero newspaces 48
Sturm bound 8517600

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Defining parameters

Level: \( N \) = \( 8450 = 2 \cdot 5^{2} \cdot 13^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(8517600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8450))\).

Total New Old
Modular forms 2142168 646481 1495687
Cusp forms 2116633 646481 1470152
Eisenstein series 25535 0 25535

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8450))\)

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
8450.2.a \(\chi_{8450}(1, \cdot)\) 8450.2.a.a 1 1
8450.2.a.b 1
8450.2.a.c 1
8450.2.a.d 1
8450.2.a.e 1
8450.2.a.f 1
8450.2.a.g 1
8450.2.a.h 1
8450.2.a.i 1
8450.2.a.j 1
8450.2.a.k 1
8450.2.a.l 1
8450.2.a.m 1
8450.2.a.n 1
8450.2.a.o 1
8450.2.a.p 1
8450.2.a.q 1
8450.2.a.r 1
8450.2.a.s 1
8450.2.a.t 1
8450.2.a.u 1
8450.2.a.v 1
8450.2.a.w 1
8450.2.a.x 1
8450.2.a.y 1
8450.2.a.z 2
8450.2.a.ba 2
8450.2.a.bb 2
8450.2.a.bc 2
8450.2.a.bd 2
8450.2.a.be 2
8450.2.a.bf 2
8450.2.a.bg 2
8450.2.a.bh 2
8450.2.a.bi 2
8450.2.a.bj 2
8450.2.a.bk 2
8450.2.a.bl 2
8450.2.a.bm 2
8450.2.a.bn 3
8450.2.a.bo 3
8450.2.a.bp 3
8450.2.a.bq 3
8450.2.a.br 3
8450.2.a.bs 3
8450.2.a.bt 3
8450.2.a.bu 3
8450.2.a.bv 3
8450.2.a.bw 3
8450.2.a.bx 3
8450.2.a.by 3
8450.2.a.bz 3
8450.2.a.ca 3
8450.2.a.cb 3
8450.2.a.cc 3
8450.2.a.cd 3
8450.2.a.ce 3
8450.2.a.cf 3
8450.2.a.cg 3
8450.2.a.ch 4
8450.2.a.ci 4
8450.2.a.cj 4
8450.2.a.ck 4
8450.2.a.cl 4
8450.2.a.cm 4
8450.2.a.cn 4
8450.2.a.co 4
8450.2.a.cp 6
8450.2.a.cq 6
8450.2.a.cr 8
8450.2.a.cs 8
8450.2.a.ct 9
8450.2.a.cu 9
8450.2.a.cv 9
8450.2.a.cw 9
8450.2.a.cx 9
8450.2.a.cy 9
8450.2.a.cz 9
8450.2.a.da 9
8450.2.b \(\chi_{8450}(7099, \cdot)\) n/a 232 1
8450.2.c \(\chi_{8450}(8449, \cdot)\) n/a 232 1
8450.2.d \(\chi_{8450}(1351, \cdot)\) n/a 242 1
8450.2.e \(\chi_{8450}(6951, \cdot)\) n/a 490 2
8450.2.g \(\chi_{8450}(3957, \cdot)\) n/a 462 2
8450.2.j \(\chi_{8450}(2943, \cdot)\) n/a 462 2
8450.2.l \(\chi_{8450}(1691, \cdot)\) n/a 1548 4
8450.2.m \(\chi_{8450}(2051, \cdot)\) n/a 488 2
8450.2.n \(\chi_{8450}(699, \cdot)\) n/a 464 2
8450.2.o \(\chi_{8450}(5599, \cdot)\) n/a 460 2
8450.2.p \(\chi_{8450}(3041, \cdot)\) n/a 1544 4
8450.2.q \(\chi_{8450}(339, \cdot)\) n/a 1552 4
8450.2.r \(\chi_{8450}(1689, \cdot)\) n/a 1536 4
8450.2.t \(\chi_{8450}(657, \cdot)\) n/a 924 4
8450.2.w \(\chi_{8450}(357, \cdot)\) n/a 924 4
8450.2.y \(\chi_{8450}(651, \cdot)\) n/a 3468 12
8450.2.z \(\chi_{8450}(191, \cdot)\) n/a 3072 8
8450.2.bb \(\chi_{8450}(577, \cdot)\) n/a 3080 8
8450.2.be \(\chi_{8450}(437, \cdot)\) n/a 3080 8
8450.2.bg \(\chi_{8450}(51, \cdot)\) n/a 3480 12
8450.2.bh \(\chi_{8450}(649, \cdot)\) n/a 3264 12
8450.2.bi \(\chi_{8450}(599, \cdot)\) n/a 3288 12
8450.2.bj \(\chi_{8450}(2389, \cdot)\) n/a 3072 8
8450.2.bk \(\chi_{8450}(529, \cdot)\) n/a 3088 8
8450.2.bl \(\chi_{8450}(361, \cdot)\) n/a 3088 8
8450.2.bm \(\chi_{8450}(451, \cdot)\) n/a 6888 24
8450.2.bo \(\chi_{8450}(307, \cdot)\) n/a 6552 24
8450.2.br \(\chi_{8450}(57, \cdot)\) n/a 6552 24
8450.2.bu \(\chi_{8450}(427, \cdot)\) n/a 6160 16
8450.2.bx \(\chi_{8450}(587, \cdot)\) n/a 6160 16
8450.2.bz \(\chi_{8450}(131, \cdot)\) n/a 21888 48
8450.2.ca \(\chi_{8450}(399, \cdot)\) n/a 6576 24
8450.2.cb \(\chi_{8450}(49, \cdot)\) n/a 6528 24
8450.2.cc \(\chi_{8450}(101, \cdot)\) n/a 6912 24
8450.2.cd \(\chi_{8450}(129, \cdot)\) n/a 21888 48
8450.2.ce \(\chi_{8450}(79, \cdot)\) n/a 21792 48
8450.2.cf \(\chi_{8450}(181, \cdot)\) n/a 21792 48
8450.2.ch \(\chi_{8450}(193, \cdot)\) n/a 13104 48
8450.2.ck \(\chi_{8450}(7, \cdot)\) n/a 13104 48
8450.2.cm \(\chi_{8450}(61, \cdot)\) n/a 43776 96
8450.2.co \(\chi_{8450}(47, \cdot)\) n/a 43680 96
8450.2.cr \(\chi_{8450}(73, \cdot)\) n/a 43680 96
8450.2.ct \(\chi_{8450}(121, \cdot)\) n/a 43584 96
8450.2.cu \(\chi_{8450}(9, \cdot)\) n/a 43584 96
8450.2.cv \(\chi_{8450}(69, \cdot)\) n/a 43776 96
8450.2.cx \(\chi_{8450}(33, \cdot)\) n/a 87360 192
8450.2.da \(\chi_{8450}(37, \cdot)\) n/a 87360 192

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8450))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8450)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(130))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(325))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(650))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(845))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1690))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4225))\)\(^{\oplus 2}\)