↑

Properties

Label 8954.2
Level 8954
Weight 2
Dimension 812825
Nonzero newspaces 36
Sturm bound 9931680

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 8954 = 2 \cdot 11^{2} \cdot 37 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 36 \)
Sturm bound: \(9931680\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8954))\).

Total New Old
Modular forms 2494440 812825 1681615
Cusp forms 2471401 812825 1658576
Eisenstein series 23039 0 23039

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8954))\)

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
8954.2.a \(\chi_{8954}(1, \cdot)\) 8954.2.a.a 1 1
8954.2.a.b 1
8954.2.a.c 1
8954.2.a.d 1
8954.2.a.e 1
8954.2.a.f 1
8954.2.a.g 1
8954.2.a.h 1
8954.2.a.i 2
8954.2.a.j 2
8954.2.a.k 2
8954.2.a.l 2
8954.2.a.m 2
8954.2.a.n 2
8954.2.a.o 2
8954.2.a.p 2
8954.2.a.q 3
8954.2.a.r 3
8954.2.a.s 3
8954.2.a.t 3
8954.2.a.u 4
8954.2.a.v 4
8954.2.a.w 4
8954.2.a.x 5
8954.2.a.y 5
8954.2.a.z 5
8954.2.a.ba 5
8954.2.a.bb 5
8954.2.a.bc 5
8954.2.a.bd 5
8954.2.a.be 6
8954.2.a.bf 6
8954.2.a.bg 7
8954.2.a.bh 7
8954.2.a.bi 7
8954.2.a.bj 7
8954.2.a.bk 12
8954.2.a.bl 12
8954.2.a.bm 14
8954.2.a.bn 14
8954.2.a.bo 14
8954.2.a.bp 14
8954.2.a.bq 16
8954.2.a.br 16
8954.2.a.bs 22
8954.2.a.bt 22
8954.2.a.bu 24
8954.2.a.bv 24
8954.2.c \(\chi_{8954}(2663, \cdot)\) n/a 346 1
8954.2.e \(\chi_{8954}(1453, \cdot)\) n/a 694 2
8954.2.f \(\chi_{8954}(2177, \cdot)\) n/a 684 2
8954.2.h \(\chi_{8954}(1703, \cdot)\) n/a 1296 4
8954.2.j \(\chi_{8954}(1211, \cdot)\) n/a 692 2
8954.2.l \(\chi_{8954}(969, \cdot)\) n/a 2070 6
8954.2.n \(\chi_{8954}(1479, \cdot)\) n/a 1368 4
8954.2.p \(\chi_{8954}(815, \cdot)\) n/a 3960 10
8954.2.r \(\chi_{8954}(1451, \cdot)\) n/a 1368 4
8954.2.s \(\chi_{8954}(269, \cdot)\) n/a 2736 8
8954.2.v \(\chi_{8954}(243, \cdot)\) n/a 2064 6
8954.2.x \(\chi_{8954}(475, \cdot)\) n/a 2736 8
8954.2.z \(\chi_{8954}(221, \cdot)\) n/a 4180 10
8954.2.bc \(\chi_{8954}(27, \cdot)\) n/a 2736 8
8954.2.be \(\chi_{8954}(507, \cdot)\) n/a 8360 20
8954.2.bg \(\chi_{8954}(241, \cdot)\) n/a 4104 12
8954.2.bi \(\chi_{8954}(43, \cdot)\) n/a 8360 20
8954.2.bj \(\chi_{8954}(9, \cdot)\) n/a 8208 24
8954.2.bk \(\chi_{8954}(75, \cdot)\) n/a 15840 40
8954.2.bl \(\chi_{8954}(717, \cdot)\) n/a 5472 16
8954.2.bo \(\chi_{8954}(397, \cdot)\) n/a 8360 20
8954.2.br \(\chi_{8954}(3, \cdot)\) n/a 8208 24
8954.2.bt \(\chi_{8954}(155, \cdot)\) n/a 25080 60
8954.2.bv \(\chi_{8954}(147, \cdot)\) n/a 16720 40
8954.2.bx \(\chi_{8954}(615, \cdot)\) n/a 16720 40
8954.2.bz \(\chi_{8954}(47, \cdot)\) n/a 33440 80
8954.2.ca \(\chi_{8954}(161, \cdot)\) n/a 16416 48
8954.2.cc \(\chi_{8954}(67, \cdot)\) n/a 25080 60
8954.2.cf \(\chi_{8954}(105, \cdot)\) n/a 33440 80
8954.2.ci \(\chi_{8954}(159, \cdot)\) n/a 33440 80
8954.2.ck \(\chi_{8954}(87, \cdot)\) n/a 50160 120
8954.2.cm \(\chi_{8954}(49, \cdot)\) n/a 100320 240
8954.2.co \(\chi_{8954}(29, \cdot)\) n/a 66880 160
8954.2.cq \(\chi_{8954}(25, \cdot)\) n/a 100320 240
8954.2.ct \(\chi_{8954}(13, \cdot)\) n/a 200640 480

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8954))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8954)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(407))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(814))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4477))\)\(^{\oplus 2}\)