Properties

Label 8673.2
Level 8673
Weight 2
Dimension 1956930
Nonzero newspaces 32
Sturm bound 10913280

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Defining parameters

Level: \( N \) = \( 8673 = 3 \cdot 7^{2} \cdot 59 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(10913280\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8673))\).

Total New Old
Modular forms 2742240 1967990 774250
Cusp forms 2714401 1956930 757471
Eisenstein series 27839 11060 16779

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8673))\)

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
8673.2.a \(\chi_{8673}(1, \cdot)\) 8673.2.a.a 1 1
8673.2.a.b 1
8673.2.a.c 1
8673.2.a.d 1
8673.2.a.e 1
8673.2.a.f 1
8673.2.a.g 1
8673.2.a.h 1
8673.2.a.i 1
8673.2.a.j 2
8673.2.a.k 2
8673.2.a.l 2
8673.2.a.m 2
8673.2.a.n 2
8673.2.a.o 3
8673.2.a.p 3
8673.2.a.q 3
8673.2.a.r 3
8673.2.a.s 3
8673.2.a.t 4
8673.2.a.u 4
8673.2.a.v 10
8673.2.a.w 11
8673.2.a.x 11
8673.2.a.y 12
8673.2.a.z 12
8673.2.a.ba 12
8673.2.a.bb 14
8673.2.a.bc 14
8673.2.a.bd 16
8673.2.a.be 16
8673.2.a.bf 17
8673.2.a.bg 17
8673.2.a.bh 20
8673.2.a.bi 20
8673.2.a.bj 20
8673.2.a.bk 20
8673.2.a.bl 26
8673.2.a.bm 26
8673.2.a.bn 30
8673.2.a.bo 30
8673.2.b \(\chi_{8673}(2890, \cdot)\) n/a 400 1
8673.2.d \(\chi_{8673}(8084, \cdot)\) n/a 772 1
8673.2.g \(\chi_{8673}(6371, \cdot)\) n/a 810 1
8673.2.i \(\chi_{8673}(2125, \cdot)\) n/a 772 2
8673.2.k \(\chi_{8673}(3362, \cdot)\) n/a 1584 2
8673.2.n \(\chi_{8673}(2420, \cdot)\) n/a 1548 2
8673.2.p \(\chi_{8673}(766, \cdot)\) n/a 800 2
8673.2.q \(\chi_{8673}(1240, \cdot)\) n/a 3240 6
8673.2.t \(\chi_{8673}(176, \cdot)\) n/a 6696 6
8673.2.u \(\chi_{8673}(650, \cdot)\) n/a 6504 6
8673.2.w \(\chi_{8673}(412, \cdot)\) n/a 3360 6
8673.2.y \(\chi_{8673}(709, \cdot)\) n/a 6504 12
8673.2.z \(\chi_{8673}(442, \cdot)\) n/a 11480 28
8673.2.bb \(\chi_{8673}(943, \cdot)\) n/a 6720 12
8673.2.bd \(\chi_{8673}(1004, \cdot)\) n/a 12984 12
8673.2.be \(\chi_{8673}(884, \cdot)\) n/a 13392 12
8673.2.bi \(\chi_{8673}(50, \cdot)\) n/a 22680 28
8673.2.bl \(\chi_{8673}(146, \cdot)\) n/a 22176 28
8673.2.bn \(\chi_{8673}(97, \cdot)\) n/a 11200 28
8673.2.bo \(\chi_{8673}(79, \cdot)\) n/a 22400 56
8673.2.bp \(\chi_{8673}(31, \cdot)\) n/a 22400 56
8673.2.br \(\chi_{8673}(68, \cdot)\) n/a 44352 56
8673.2.bu \(\chi_{8673}(128, \cdot)\) n/a 44352 56
8673.2.bw \(\chi_{8673}(22, \cdot)\) n/a 94080 168
8673.2.by \(\chi_{8673}(13, \cdot)\) n/a 94080 168
8673.2.ca \(\chi_{8673}(20, \cdot)\) n/a 187488 168
8673.2.cb \(\chi_{8673}(8, \cdot)\) n/a 187488 168
8673.2.ce \(\chi_{8673}(4, \cdot)\) n/a 188160 336
8673.2.ch \(\chi_{8673}(2, \cdot)\) n/a 374976 336
8673.2.ci \(\chi_{8673}(5, \cdot)\) n/a 374976 336
8673.2.ck \(\chi_{8673}(10, \cdot)\) n/a 188160 336

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8673))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8673)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(177))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(413))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1239))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2891))\)\(^{\oplus 2}\)