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Properties

Label 6728.2
Level 6728
Weight 2
Dimension 790559
Nonzero newspaces 20
Sturm bound 5651520

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Defining parameters

Level: \( N \) = \( 6728 = 2^{3} \cdot 29^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(5651520\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6728))\).

Total New Old
Modular forms 1420104 795153 624951
Cusp forms 1405657 790559 615098
Eisenstein series 14447 4594 9853

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6728))\)

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
6728.2.a \(\chi_{6728}(1, \cdot)\) 6728.2.a.a 1 1
6728.2.a.b 1
6728.2.a.c 1
6728.2.a.d 1
6728.2.a.e 2
6728.2.a.f 2
6728.2.a.g 2
6728.2.a.h 3
6728.2.a.i 3
6728.2.a.j 3
6728.2.a.k 3
6728.2.a.l 3
6728.2.a.m 3
6728.2.a.n 3
6728.2.a.o 3
6728.2.a.p 3
6728.2.a.q 3
6728.2.a.r 3
6728.2.a.s 4
6728.2.a.t 4
6728.2.a.u 6
6728.2.a.v 6
6728.2.a.w 6
6728.2.a.x 6
6728.2.a.y 12
6728.2.a.z 12
6728.2.a.ba 12
6728.2.a.bb 12
6728.2.a.bc 16
6728.2.a.bd 16
6728.2.a.be 24
6728.2.a.bf 24
6728.2.c \(\chi_{6728}(3365, \cdot)\) n/a 784 1
6728.2.e \(\chi_{6728}(1681, \cdot)\) n/a 202 1
6728.2.g \(\chi_{6728}(5045, \cdot)\) n/a 784 1
6728.2.i \(\chi_{6728}(5087, \cdot)\) None 0 2
6728.2.k \(\chi_{6728}(1723, \cdot)\) n/a 1568 2
6728.2.m \(\chi_{6728}(2713, \cdot)\) n/a 1218 6
6728.2.o \(\chi_{6728}(1037, \cdot)\) n/a 4704 6
6728.2.q \(\chi_{6728}(1745, \cdot)\) n/a 1212 6
6728.2.s \(\chi_{6728}(605, \cdot)\) n/a 4704 6
6728.2.v \(\chi_{6728}(467, \cdot)\) n/a 9408 12
6728.2.x \(\chi_{6728}(855, \cdot)\) None 0 12
6728.2.y \(\chi_{6728}(233, \cdot)\) n/a 6076 28
6728.2.ba \(\chi_{6728}(173, \cdot)\) n/a 24304 28
6728.2.bc \(\chi_{6728}(57, \cdot)\) n/a 6104 28
6728.2.be \(\chi_{6728}(117, \cdot)\) n/a 24304 28
6728.2.bh \(\chi_{6728}(75, \cdot)\) n/a 48608 56
6728.2.bj \(\chi_{6728}(191, \cdot)\) None 0 56
6728.2.bk \(\chi_{6728}(25, \cdot)\) n/a 36456 168
6728.2.bm \(\chi_{6728}(45, \cdot)\) n/a 145824 168
6728.2.bo \(\chi_{6728}(9, \cdot)\) n/a 36624 168
6728.2.bq \(\chi_{6728}(5, \cdot)\) n/a 145824 168
6728.2.bs \(\chi_{6728}(15, \cdot)\) None 0 336
6728.2.bu \(\chi_{6728}(3, \cdot)\) n/a 291648 336

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6728))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6728)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(232))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(841))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1682))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3364))\)\(^{\oplus 2}\)