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Properties

Label 8032.2
Level 8032
Weight 2
Dimension 1131474
Nonzero newspaces 24
Sturm bound 8064000

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Defining parameters

Level: \( N \) = \( 8032 = 2^{5} \cdot 251 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(8064000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8032))\).

Total New Old
Modular forms 2024000 1136454 887546
Cusp forms 2008001 1131474 876527
Eisenstein series 15999 4980 11019

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8032))\)

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
8032.2.a \(\chi_{8032}(1, \cdot)\) 8032.2.a.a 1 1
8032.2.a.b 1
8032.2.a.c 1
8032.2.a.d 1
8032.2.a.e 28
8032.2.a.f 28
8032.2.a.g 30
8032.2.a.h 30
8032.2.a.i 30
8032.2.a.j 30
8032.2.a.k 35
8032.2.a.l 35
8032.2.b \(\chi_{8032}(4017, \cdot)\) n/a 250 1
8032.2.e \(\chi_{8032}(8031, \cdot)\) n/a 252 1
8032.2.f \(\chi_{8032}(4015, \cdot)\) n/a 250 1
8032.2.j \(\chi_{8032}(2009, \cdot)\) None 0 2
8032.2.k \(\chi_{8032}(2007, \cdot)\) None 0 2
8032.2.m \(\chi_{8032}(1153, \cdot)\) n/a 1008 4
8032.2.o \(\chi_{8032}(1005, \cdot)\) n/a 4000 4
8032.2.p \(\chi_{8032}(1003, \cdot)\) n/a 4024 4
8032.2.s \(\chi_{8032}(2863, \cdot)\) n/a 1000 4
8032.2.v \(\chi_{8032}(113, \cdot)\) n/a 1000 4
8032.2.w \(\chi_{8032}(2239, \cdot)\) n/a 1008 4
8032.2.z \(\chi_{8032}(231, \cdot)\) None 0 8
8032.2.ba \(\chi_{8032}(2121, \cdot)\) None 0 8
8032.2.bc \(\chi_{8032}(769, \cdot)\) n/a 5040 20
8032.2.be \(\chi_{8032}(283, \cdot)\) n/a 16096 16
8032.2.bf \(\chi_{8032}(149, \cdot)\) n/a 16096 16
8032.2.bh \(\chi_{8032}(1663, \cdot)\) n/a 5040 20
8032.2.bk \(\chi_{8032}(47, \cdot)\) n/a 5000 20
8032.2.bl \(\chi_{8032}(241, \cdot)\) n/a 5000 20
8032.2.bo \(\chi_{8032}(25, \cdot)\) None 0 40
8032.2.bp \(\chi_{8032}(151, \cdot)\) None 0 40
8032.2.bs \(\chi_{8032}(65, \cdot)\) n/a 25200 100
8032.2.bv \(\chi_{8032}(5, \cdot)\) n/a 80480 80
8032.2.bw \(\chi_{8032}(171, \cdot)\) n/a 80480 80
8032.2.by \(\chi_{8032}(95, \cdot)\) n/a 25200 100
8032.2.ca \(\chi_{8032}(111, \cdot)\) n/a 25000 100
8032.2.cc \(\chi_{8032}(17, \cdot)\) n/a 25000 100
8032.2.cg \(\chi_{8032}(9, \cdot)\) None 0 200
8032.2.ch \(\chi_{8032}(55, \cdot)\) None 0 200
8032.2.cj \(\chi_{8032}(11, \cdot)\) n/a 402400 400
8032.2.ck \(\chi_{8032}(13, \cdot)\) n/a 402400 400

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8032))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8032)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(251))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(502))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1004))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2008))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4016))\)\(^{\oplus 2}\)