Properties

Label 6378.2
Level 6378
Weight 2
Dimension 282493
Nonzero newspaces 12
Sturm bound 4519872

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Defining parameters

Level: \( N \) = \( 6378 = 2 \cdot 3 \cdot 1063 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(4519872\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6378))\).

Total New Old
Modular forms 1134216 282493 851723
Cusp forms 1125721 282493 843228
Eisenstein series 8495 0 8495

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6378))\)

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
6378.2.a \(\chi_{6378}(1, \cdot)\) 6378.2.a.a 1 1
6378.2.a.b 1
6378.2.a.c 1
6378.2.a.d 1
6378.2.a.e 1
6378.2.a.f 1
6378.2.a.g 2
6378.2.a.h 12
6378.2.a.i 16
6378.2.a.j 21
6378.2.a.k 21
6378.2.a.l 23
6378.2.a.m 23
6378.2.a.n 26
6378.2.a.o 27
6378.2.d \(\chi_{6378}(6377, \cdot)\) n/a 356 1
6378.2.e \(\chi_{6378}(343, \cdot)\) n/a 352 2
6378.2.h \(\chi_{6378}(3533, \cdot)\) n/a 712 2
6378.2.i \(\chi_{6378}(7, \cdot)\) n/a 1068 6
6378.2.j \(\chi_{6378}(911, \cdot)\) n/a 2124 6
6378.2.m \(\chi_{6378}(157, \cdot)\) n/a 10208 58
6378.2.n \(\chi_{6378}(125, \cdot)\) n/a 20648 58
6378.2.q \(\chi_{6378}(13, \cdot)\) n/a 20416 116
6378.2.r \(\chi_{6378}(5, \cdot)\) n/a 41296 116
6378.2.u \(\chi_{6378}(19, \cdot)\) n/a 61944 348
6378.2.x \(\chi_{6378}(29, \cdot)\) n/a 123192 348

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6378))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6378)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1063))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2126))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3189))\)\(^{\oplus 2}\)