Properties

Label 6724.2
Level 6724
Weight 2
Dimension 820350
Nonzero newspaces 16
Sturm bound 5648160

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 6724 = 2^{2} \cdot 41^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(5648160\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6724))\).

Total New Old
Modular forms 1418140 825070 593070
Cusp forms 1405941 820350 585591
Eisenstein series 12199 4720 7479

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6724))\)

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
6724.2.a \(\chi_{6724}(1, \cdot)\) 6724.2.a.a 3 1
6724.2.a.b 3
6724.2.a.c 4
6724.2.a.d 4
6724.2.a.e 6
6724.2.a.f 8
6724.2.a.g 8
6724.2.a.h 12
6724.2.a.i 12
6724.2.a.j 16
6724.2.a.k 18
6724.2.a.l 18
6724.2.a.m 24
6724.2.b \(\chi_{6724}(3361, \cdot)\) n/a 136 1
6724.2.f \(\chi_{6724}(4665, \cdot)\) n/a 274 2
6724.2.g \(\chi_{6724}(857, \cdot)\) n/a 544 4
6724.2.i \(\chi_{6724}(847, \cdot)\) n/a 3124 4
6724.2.k \(\chi_{6724}(761, \cdot)\) n/a 544 4
6724.2.m \(\chi_{6724}(3569, \cdot)\) n/a 1096 8
6724.2.o \(\chi_{6724}(719, \cdot)\) n/a 12496 16
6724.2.q \(\chi_{6724}(165, \cdot)\) n/a 5760 40
6724.2.t \(\chi_{6724}(81, \cdot)\) n/a 5760 40
6724.2.u \(\chi_{6724}(9, \cdot)\) n/a 11440 80
6724.2.w \(\chi_{6724}(37, \cdot)\) n/a 23040 160
6724.2.x \(\chi_{6724}(3, \cdot)\) n/a 137440 160
6724.2.ba \(\chi_{6724}(25, \cdot)\) n/a 23040 160
6724.2.bd \(\chi_{6724}(5, \cdot)\) n/a 45760 320
6724.2.bf \(\chi_{6724}(7, \cdot)\) n/a 549760 640

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6724))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6724)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(82))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(164))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1681))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3362))\)\(^{\oplus 2}\)