Properties

Label 7168.2
Level 7168
Weight 2
Dimension 845472
Nonzero newspaces 32
Sturm bound 6291456

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Defining parameters

Level: \( N \) = \( 7168 = 2^{10} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 32 \)
Sturm bound: \(6291456\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7168))\).

Total New Old
Modular forms 1582848 850272 732576
Cusp forms 1562881 845472 717409
Eisenstein series 19967 4800 15167

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7168))\)

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
7168.2.a \(\chi_{7168}(1, \cdot)\) 7168.2.a.a 2 1
7168.2.a.b 2
7168.2.a.c 2
7168.2.a.d 2
7168.2.a.e 2
7168.2.a.f 2
7168.2.a.g 2
7168.2.a.h 2
7168.2.a.i 2
7168.2.a.j 2
7168.2.a.k 2
7168.2.a.l 2
7168.2.a.m 2
7168.2.a.n 2
7168.2.a.o 2
7168.2.a.p 2
7168.2.a.q 2
7168.2.a.r 2
7168.2.a.s 4
7168.2.a.t 4
7168.2.a.u 4
7168.2.a.v 4
7168.2.a.w 4
7168.2.a.x 4
7168.2.a.y 6
7168.2.a.z 6
7168.2.a.ba 8
7168.2.a.bb 8
7168.2.a.bc 8
7168.2.a.bd 8
7168.2.a.be 8
7168.2.a.bf 8
7168.2.a.bg 12
7168.2.a.bh 12
7168.2.a.bi 12
7168.2.a.bj 12
7168.2.a.bk 12
7168.2.a.bl 12
7168.2.b \(\chi_{7168}(3585, \cdot)\) n/a 192 1
7168.2.e \(\chi_{7168}(3583, \cdot)\) n/a 248 1
7168.2.f \(\chi_{7168}(7167, \cdot)\) n/a 248 1
7168.2.i \(\chi_{7168}(4097, \cdot)\) n/a 496 2
7168.2.j \(\chi_{7168}(1791, \cdot)\) n/a 496 2
7168.2.m \(\chi_{7168}(1793, \cdot)\) n/a 384 2
7168.2.p \(\chi_{7168}(2047, \cdot)\) n/a 496 2
7168.2.q \(\chi_{7168}(5631, \cdot)\) n/a 496 2
7168.2.t \(\chi_{7168}(513, \cdot)\) n/a 496 2
7168.2.u \(\chi_{7168}(897, \cdot)\) n/a 768 4
7168.2.x \(\chi_{7168}(895, \cdot)\) n/a 1024 4
7168.2.z \(\chi_{7168}(255, \cdot)\) n/a 992 4
7168.2.ba \(\chi_{7168}(2305, \cdot)\) n/a 992 4
7168.2.bc \(\chi_{7168}(449, \cdot)\) n/a 1536 8
7168.2.bd \(\chi_{7168}(447, \cdot)\) n/a 1984 8
7168.2.bh \(\chi_{7168}(641, \cdot)\) n/a 2048 8
7168.2.bi \(\chi_{7168}(383, \cdot)\) n/a 2048 8
7168.2.bk \(\chi_{7168}(223, \cdot)\) n/a 4032 16
7168.2.bn \(\chi_{7168}(225, \cdot)\) n/a 3072 16
7168.2.bq \(\chi_{7168}(703, \cdot)\) n/a 3968 16
7168.2.br \(\chi_{7168}(65, \cdot)\) n/a 3968 16
7168.2.bs \(\chi_{7168}(113, \cdot)\) n/a 6144 32
7168.2.bv \(\chi_{7168}(111, \cdot)\) n/a 8128 32
7168.2.bx \(\chi_{7168}(31, \cdot)\) n/a 8064 32
7168.2.by \(\chi_{7168}(289, \cdot)\) n/a 8064 32
7168.2.ca \(\chi_{7168}(57, \cdot)\) None 0 64
7168.2.cb \(\chi_{7168}(55, \cdot)\) None 0 64
7168.2.cf \(\chi_{7168}(81, \cdot)\) n/a 16256 64
7168.2.cg \(\chi_{7168}(47, \cdot)\) n/a 16256 64
7168.2.ci \(\chi_{7168}(27, \cdot)\) n/a 130816 128
7168.2.cl \(\chi_{7168}(29, \cdot)\) n/a 98304 128
7168.2.co \(\chi_{7168}(87, \cdot)\) None 0 128
7168.2.cp \(\chi_{7168}(9, \cdot)\) None 0 128
7168.2.cr \(\chi_{7168}(3, \cdot)\) n/a 261632 256
7168.2.cs \(\chi_{7168}(37, \cdot)\) n/a 261632 256

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7168))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7168)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(256))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(448))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(512))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(896))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1024))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1792))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3584))\)\(^{\oplus 2}\)