Properties

Label 8993.2
Level 8993
Weight 2
Dimension 3305330
Nonzero newspaces 20
Sturm bound 13406976

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Defining parameters

Level: \( N \) = \( 8993 = 17 \cdot 23^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(13406976\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8993))\).

Total New Old
Modular forms 3363712 3326464 37248
Cusp forms 3339777 3305330 34447
Eisenstein series 23935 21134 2801

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8993))\)

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
8993.2.a \(\chi_{8993}(1, \cdot)\) 8993.2.a.a 1 1
8993.2.a.b 2
8993.2.a.c 3
8993.2.a.d 3
8993.2.a.e 4
8993.2.a.f 4
8993.2.a.g 9
8993.2.a.h 11
8993.2.a.i 11
8993.2.a.j 12
8993.2.a.k 14
8993.2.a.l 14
8993.2.a.m 15
8993.2.a.n 15
8993.2.a.o 28
8993.2.a.p 28
8993.2.a.q 30
8993.2.a.r 30
8993.2.a.s 60
8993.2.a.t 60
8993.2.a.u 70
8993.2.a.v 70
8993.2.a.w 90
8993.2.a.x 90
8993.2.b \(\chi_{8993}(8465, \cdot)\) n/a 736 1
8993.2.e \(\chi_{8993}(3175, \cdot)\) n/a 1472 2
8993.2.g \(\chi_{8993}(2117, \cdot)\) n/a 2948 4
8993.2.i \(\chi_{8993}(647, \cdot)\) n/a 6720 10
8993.2.k \(\chi_{8993}(1057, \cdot)\) n/a 5888 8
8993.2.n \(\chi_{8993}(118, \cdot)\) n/a 7360 10
8993.2.o \(\chi_{8993}(392, \cdot)\) n/a 16192 22
8993.2.q \(\chi_{8993}(795, \cdot)\) n/a 14720 20
8993.2.t \(\chi_{8993}(254, \cdot)\) n/a 18172 22
8993.2.v \(\chi_{8993}(399, \cdot)\) n/a 29440 40
8993.2.x \(\chi_{8993}(47, \cdot)\) n/a 36344 44
8993.2.y \(\chi_{8993}(28, \cdot)\) n/a 58880 80
8993.2.bb \(\chi_{8993}(70, \cdot)\) n/a 72688 88
8993.2.bc \(\chi_{8993}(18, \cdot)\) n/a 161920 220
8993.2.bd \(\chi_{8993}(22, \cdot)\) n/a 145376 176
8993.2.bf \(\chi_{8993}(16, \cdot)\) n/a 181720 220
8993.2.bi \(\chi_{8993}(4, \cdot)\) n/a 363440 440
8993.2.bk \(\chi_{8993}(2, \cdot)\) n/a 726880 880
8993.2.bn \(\chi_{8993}(5, \cdot)\) n/a 1453760 1760

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8993))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8993)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(391))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(529))\)\(^{\oplus 2}\)