Properties

Label 8016.2
Level 8016
Weight 2
Dimension 751436
Nonzero newspaces 16
Sturm bound 7139328

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Defining parameters

Level: \( N \) = \( 8016 = 2^{4} \cdot 3 \cdot 167 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(7139328\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8016))\).

Total New Old
Modular forms 1794128 754408 1039720
Cusp forms 1775537 751436 1024101
Eisenstein series 18591 2972 15619

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8016))\)

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
8016.2.a \(\chi_{8016}(1, \cdot)\) 8016.2.a.a 1 1
8016.2.a.b 1
8016.2.a.c 1
8016.2.a.d 1
8016.2.a.e 1
8016.2.a.f 1
8016.2.a.g 1
8016.2.a.h 1
8016.2.a.i 1
8016.2.a.j 1
8016.2.a.k 2
8016.2.a.l 3
8016.2.a.m 3
8016.2.a.n 3
8016.2.a.o 4
8016.2.a.p 5
8016.2.a.q 5
8016.2.a.r 5
8016.2.a.s 5
8016.2.a.t 5
8016.2.a.u 5
8016.2.a.v 7
8016.2.a.w 7
8016.2.a.x 8
8016.2.a.y 8
8016.2.a.z 8
8016.2.a.ba 9
8016.2.a.bb 9
8016.2.a.bc 9
8016.2.a.bd 10
8016.2.a.be 11
8016.2.a.bf 12
8016.2.a.bg 13
8016.2.b \(\chi_{8016}(2671, \cdot)\) n/a 168 1
8016.2.e \(\chi_{8016}(335, \cdot)\) n/a 332 1
8016.2.f \(\chi_{8016}(4009, \cdot)\) None 0 1
8016.2.i \(\chi_{8016}(1001, \cdot)\) None 0 1
8016.2.j \(\chi_{8016}(4343, \cdot)\) None 0 1
8016.2.m \(\chi_{8016}(6679, \cdot)\) None 0 1
8016.2.n \(\chi_{8016}(5009, \cdot)\) n/a 334 1
8016.2.s \(\chi_{8016}(3005, \cdot)\) n/a 2680 2
8016.2.t \(\chi_{8016}(2005, \cdot)\) n/a 1328 2
8016.2.u \(\chi_{8016}(667, \cdot)\) n/a 1344 2
8016.2.v \(\chi_{8016}(2339, \cdot)\) n/a 2656 2
8016.2.y \(\chi_{8016}(49, \cdot)\) n/a 13776 82
8016.2.bb \(\chi_{8016}(17, \cdot)\) n/a 27388 82
8016.2.bc \(\chi_{8016}(55, \cdot)\) None 0 82
8016.2.bf \(\chi_{8016}(215, \cdot)\) None 0 82
8016.2.bg \(\chi_{8016}(41, \cdot)\) None 0 82
8016.2.bj \(\chi_{8016}(25, \cdot)\) None 0 82
8016.2.bk \(\chi_{8016}(47, \cdot)\) n/a 27552 82
8016.2.bn \(\chi_{8016}(79, \cdot)\) n/a 13776 82
8016.2.bq \(\chi_{8016}(11, \cdot)\) n/a 219760 164
8016.2.br \(\chi_{8016}(43, \cdot)\) n/a 110208 164
8016.2.bs \(\chi_{8016}(61, \cdot)\) n/a 110208 164
8016.2.bt \(\chi_{8016}(5, \cdot)\) n/a 219760 164

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8016))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8016)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(167))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(334))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(501))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(668))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1002))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1336))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2004))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2672))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4008))\)\(^{\oplus 2}\)