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Properties

Label 8670.2
Level 8670
Weight 2
Dimension 454616
Nonzero newspaces 36
Sturm bound 7990272

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Defining parameters

Level: \( N \) = \( 8670 = 2 \cdot 3 \cdot 5 \cdot 17^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 36 \)
Sturm bound: \(7990272\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8670))\).

Total New Old
Modular forms 2010368 454616 1555752
Cusp forms 1984769 454616 1530153
Eisenstein series 25599 0 25599

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8670))\)

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
8670.2.a \(\chi_{8670}(1, \cdot)\) 8670.2.a.a 1 1
8670.2.a.b 1
8670.2.a.c 1
8670.2.a.d 1
8670.2.a.e 1
8670.2.a.f 1
8670.2.a.g 1
8670.2.a.h 1
8670.2.a.i 1
8670.2.a.j 1
8670.2.a.k 1
8670.2.a.l 1
8670.2.a.m 1
8670.2.a.n 1
8670.2.a.o 1
8670.2.a.p 1
8670.2.a.q 1
8670.2.a.r 1
8670.2.a.s 1
8670.2.a.t 1
8670.2.a.u 1
8670.2.a.v 1
8670.2.a.w 1
8670.2.a.x 1
8670.2.a.y 1
8670.2.a.z 1
8670.2.a.ba 1
8670.2.a.bb 1
8670.2.a.bc 2
8670.2.a.bd 2
8670.2.a.be 2
8670.2.a.bf 2
8670.2.a.bg 2
8670.2.a.bh 2
8670.2.a.bi 2
8670.2.a.bj 2
8670.2.a.bk 2
8670.2.a.bl 3
8670.2.a.bm 3
8670.2.a.bn 3
8670.2.a.bo 3
8670.2.a.bp 3
8670.2.a.bq 3
8670.2.a.br 3
8670.2.a.bs 3
8670.2.a.bt 4
8670.2.a.bu 4
8670.2.a.bv 4
8670.2.a.bw 4
8670.2.a.bx 4
8670.2.a.by 4
8670.2.a.bz 4
8670.2.a.ca 4
8670.2.a.cb 6
8670.2.a.cc 6
8670.2.a.cd 6
8670.2.a.ce 6
8670.2.a.cf 6
8670.2.a.cg 6
8670.2.a.ch 6
8670.2.a.ci 6
8670.2.a.cj 8
8670.2.a.ck 8
8670.2.a.cl 8
8670.2.a.cm 8
8670.2.c \(\chi_{8670}(2311, \cdot)\) n/a 180 1
8670.2.d \(\chi_{8670}(3469, \cdot)\) n/a 270 1
8670.2.f \(\chi_{8670}(5779, \cdot)\) n/a 268 1
8670.2.i \(\chi_{8670}(5453, \cdot)\) n/a 1080 2
8670.2.l \(\chi_{8670}(1157, \cdot)\) n/a 1084 2
8670.2.m \(\chi_{8670}(829, \cdot)\) n/a 536 2
8670.2.p \(\chi_{8670}(4951, \cdot)\) n/a 360 2
8670.2.q \(\chi_{8670}(1733, \cdot)\) n/a 1080 2
8670.2.t \(\chi_{8670}(4373, \cdot)\) n/a 1080 2
8670.2.u \(\chi_{8670}(2491, \cdot)\) n/a 720 4
8670.2.w \(\chi_{8670}(1913, \cdot)\) n/a 2160 4
8670.2.z \(\chi_{8670}(977, \cdot)\) n/a 2160 4
8670.2.bb \(\chi_{8670}(1579, \cdot)\) n/a 1088 4
8670.2.bd \(\chi_{8670}(643, \cdot)\) n/a 2160 8
8670.2.bf \(\chi_{8670}(131, \cdot)\) n/a 2880 8
8670.2.bh \(\chi_{8670}(329, \cdot)\) n/a 4320 8
8670.2.bi \(\chi_{8670}(2377, \cdot)\) n/a 2160 8
8670.2.bk \(\chi_{8670}(511, \cdot)\) n/a 3264 16
8670.2.bn \(\chi_{8670}(169, \cdot)\) n/a 4928 16
8670.2.bp \(\chi_{8670}(409, \cdot)\) n/a 4928 16
8670.2.bq \(\chi_{8670}(271, \cdot)\) n/a 3264 16
8670.2.bs \(\chi_{8670}(47, \cdot)\) n/a 19584 32
8670.2.bv \(\chi_{8670}(203, \cdot)\) n/a 19584 32
8670.2.bw \(\chi_{8670}(361, \cdot)\) n/a 6528 32
8670.2.bz \(\chi_{8670}(259, \cdot)\) n/a 9856 32
8670.2.ca \(\chi_{8670}(137, \cdot)\) n/a 19584 32
8670.2.cd \(\chi_{8670}(353, \cdot)\) n/a 19584 32
8670.2.ce \(\chi_{8670}(19, \cdot)\) n/a 19456 64
8670.2.cg \(\chi_{8670}(53, \cdot)\) n/a 39168 64
8670.2.cj \(\chi_{8670}(257, \cdot)\) n/a 39168 64
8670.2.cl \(\chi_{8670}(121, \cdot)\) n/a 13056 64
8670.2.cn \(\chi_{8670}(37, \cdot)\) n/a 39168 128
8670.2.co \(\chi_{8670}(29, \cdot)\) n/a 78336 128
8670.2.cq \(\chi_{8670}(11, \cdot)\) n/a 52224 128
8670.2.cs \(\chi_{8670}(7, \cdot)\) n/a 39168 128

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8670))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8670)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(170))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(255))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(289))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(510))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(578))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(867))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1445))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1734))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2890))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4335))\)\(^{\oplus 2}\)