Properties

Label 8043.2
Level 8043
Weight 2
Dimension 1683083
Nonzero newspaces 16
Sturm bound 9388032

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Defining parameters

Level: \( N \) = \( 8043 = 3 \cdot 7 \cdot 383 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(9388032\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8043))\).

Total New Old
Modular forms 2356176 1690699 665477
Cusp forms 2337841 1683083 654758
Eisenstein series 18335 7616 10719

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8043))\)

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
8043.2.a \(\chi_{8043}(1, \cdot)\) 8043.2.a.a 1 1
8043.2.a.b 1
8043.2.a.c 1
8043.2.a.d 1
8043.2.a.e 1
8043.2.a.f 1
8043.2.a.g 1
8043.2.a.h 1
8043.2.a.i 1
8043.2.a.j 1
8043.2.a.k 1
8043.2.a.l 2
8043.2.a.m 3
8043.2.a.n 40
8043.2.a.o 41
8043.2.a.p 41
8043.2.a.q 44
8043.2.a.r 46
8043.2.a.s 50
8043.2.a.t 52
8043.2.a.u 53
8043.2.d \(\chi_{8043}(3065, \cdot)\) n/a 1020 1
8043.2.e \(\chi_{8043}(2297, \cdot)\) n/a 768 1
8043.2.h \(\chi_{8043}(2680, \cdot)\) n/a 512 1
8043.2.i \(\chi_{8043}(1150, \cdot)\) n/a 1020 2
8043.2.j \(\chi_{8043}(1531, \cdot)\) n/a 1024 2
8043.2.m \(\chi_{8043}(3446, \cdot)\) n/a 2040 2
8043.2.n \(\chi_{8043}(1916, \cdot)\) n/a 2036 2
8043.2.q \(\chi_{8043}(43, \cdot)\) n/a 72960 190
8043.2.r \(\chi_{8043}(13, \cdot)\) n/a 97280 190
8043.2.u \(\chi_{8043}(155, \cdot)\) n/a 145920 190
8043.2.v \(\chi_{8043}(62, \cdot)\) n/a 193800 190
8043.2.y \(\chi_{8043}(4, \cdot)\) n/a 194560 380
8043.2.bb \(\chi_{8043}(17, \cdot)\) n/a 387600 380
8043.2.bc \(\chi_{8043}(11, \cdot)\) n/a 387600 380
8043.2.bf \(\chi_{8043}(10, \cdot)\) n/a 194560 380

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8043))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8043)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(383))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1149))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2681))\)\(^{\oplus 2}\)