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Properties

Label 4067.2
Level 4067
Weight 2
Dimension 643644
Nonzero newspaces 16
Sturm bound 2700096

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Defining parameters

Level: \( N \) = \( 4067 = 7^{2} \cdot 83 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(2700096\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4067))\).

Total New Old
Modular forms 679944 651500 28444
Cusp forms 670105 643644 26461
Eisenstein series 9839 7856 1983

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4067))\)

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
4067.2.a \(\chi_{4067}(1, \cdot)\) 4067.2.a.a 1 1
4067.2.a.b 1
4067.2.a.c 1
4067.2.a.d 6
4067.2.a.e 7
4067.2.a.f 7
4067.2.a.g 13
4067.2.a.h 14
4067.2.a.i 20
4067.2.a.j 20
4067.2.a.k 20
4067.2.a.l 20
4067.2.a.m 33
4067.2.a.n 33
4067.2.a.o 42
4067.2.a.p 42
4067.2.b \(\chi_{4067}(4066, \cdot)\) n/a 276 1
4067.2.e \(\chi_{4067}(2076, \cdot)\) n/a 548 2
4067.2.h \(\chi_{4067}(1244, \cdot)\) n/a 552 2
4067.2.i \(\chi_{4067}(582, \cdot)\) n/a 2304 6
4067.2.l \(\chi_{4067}(580, \cdot)\) n/a 2340 6
4067.2.m \(\chi_{4067}(333, \cdot)\) n/a 4584 12
4067.2.n \(\chi_{4067}(99, \cdot)\) n/a 11280 40
4067.2.o \(\chi_{4067}(82, \cdot)\) n/a 4680 12
4067.2.t \(\chi_{4067}(97, \cdot)\) n/a 11040 40
4067.2.u \(\chi_{4067}(30, \cdot)\) n/a 22080 80
4067.2.v \(\chi_{4067}(19, \cdot)\) n/a 22080 80
4067.2.y \(\chi_{4067}(29, \cdot)\) n/a 93600 240
4067.2.z \(\chi_{4067}(6, \cdot)\) n/a 93600 240
4067.2.bc \(\chi_{4067}(4, \cdot)\) n/a 187200 480
4067.2.bf \(\chi_{4067}(5, \cdot)\) n/a 187200 480

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4067))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4067)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(83))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(581))\)\(^{\oplus 2}\)