Properties

Label 5312.2
Level 5312
Weight 2
Dimension 494010
Nonzero newspaces 16
Sturm bound 3526656

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Defining parameters

Level: \( N \) = \( 5312 = 2^{6} \cdot 83 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(3526656\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5312))\).

Total New Old
Modular forms 887568 497574 389994
Cusp forms 875761 494010 381751
Eisenstein series 11807 3564 8243

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5312))\)

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
5312.2.a \(\chi_{5312}(1, \cdot)\) 5312.2.a.a 1 1
5312.2.a.b 1
5312.2.a.c 1
5312.2.a.d 1
5312.2.a.e 1
5312.2.a.f 1
5312.2.a.g 1
5312.2.a.h 1
5312.2.a.i 1
5312.2.a.j 1
5312.2.a.k 1
5312.2.a.l 1
5312.2.a.m 1
5312.2.a.n 1
5312.2.a.o 1
5312.2.a.p 1
5312.2.a.q 2
5312.2.a.r 2
5312.2.a.s 2
5312.2.a.t 2
5312.2.a.u 2
5312.2.a.v 2
5312.2.a.w 2
5312.2.a.x 2
5312.2.a.y 3
5312.2.a.z 3
5312.2.a.ba 3
5312.2.a.bb 3
5312.2.a.bc 3
5312.2.a.bd 3
5312.2.a.be 4
5312.2.a.bf 4
5312.2.a.bg 4
5312.2.a.bh 4
5312.2.a.bi 5
5312.2.a.bj 5
5312.2.a.bk 5
5312.2.a.bl 5
5312.2.a.bm 6
5312.2.a.bn 6
5312.2.a.bo 6
5312.2.a.bp 6
5312.2.a.bq 8
5312.2.a.br 8
5312.2.a.bs 8
5312.2.a.bt 8
5312.2.a.bu 11
5312.2.a.bv 11
5312.2.b \(\chi_{5312}(5311, \cdot)\) n/a 166 1
5312.2.c \(\chi_{5312}(2657, \cdot)\) n/a 164 1
5312.2.h \(\chi_{5312}(2655, \cdot)\) n/a 168 1
5312.2.j \(\chi_{5312}(1329, \cdot)\) n/a 328 2
5312.2.l \(\chi_{5312}(1327, \cdot)\) n/a 332 2
5312.2.m \(\chi_{5312}(663, \cdot)\) None 0 4
5312.2.n \(\chi_{5312}(665, \cdot)\) None 0 4
5312.2.q \(\chi_{5312}(333, \cdot)\) n/a 5248 8
5312.2.t \(\chi_{5312}(331, \cdot)\) n/a 5360 8
5312.2.u \(\chi_{5312}(65, \cdot)\) n/a 6640 40
5312.2.v \(\chi_{5312}(159, \cdot)\) n/a 6720 40
5312.2.ba \(\chi_{5312}(33, \cdot)\) n/a 6720 40
5312.2.bb \(\chi_{5312}(255, \cdot)\) n/a 6640 40
5312.2.bc \(\chi_{5312}(15, \cdot)\) n/a 13280 80
5312.2.be \(\chi_{5312}(17, \cdot)\) n/a 13280 80
5312.2.bi \(\chi_{5312}(9, \cdot)\) None 0 160
5312.2.bj \(\chi_{5312}(39, \cdot)\) None 0 160
5312.2.bk \(\chi_{5312}(19, \cdot)\) n/a 214400 320
5312.2.bn \(\chi_{5312}(21, \cdot)\) n/a 214400 320

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5312))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5312)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(83))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(166))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(332))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(664))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1328))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2656))\)\(^{\oplus 2}\)