Properties

Label 4034.2
Level 4034
Weight 2
Dimension 169511
Nonzero newspaces 30
Sturm bound 2034144

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Defining parameters

Level: \( N \) = \( 4034 = 2 \cdot 2017 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(2034144\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4034))\).

Total New Old
Modular forms 510552 169511 341041
Cusp forms 506521 169511 337010
Eisenstein series 4031 0 4031

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4034))\)

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
4034.2.a \(\chi_{4034}(1, \cdot)\) 4034.2.a.a 33 1
4034.2.a.b 35
4034.2.a.c 49
4034.2.a.d 52
4034.2.b \(\chi_{4034}(4033, \cdot)\) n/a 170 1
4034.2.c \(\chi_{4034}(2311, \cdot)\) n/a 340 2
4034.2.d \(\chi_{4034}(229, \cdot)\) n/a 340 2
4034.2.e \(\chi_{4034}(295, \cdot)\) n/a 340 2
4034.2.f \(\chi_{4034}(79, \cdot)\) n/a 1020 6
4034.2.g \(\chi_{4034}(1469, \cdot)\) n/a 680 4
4034.2.h \(\chi_{4034}(1005, \cdot)\) n/a 1008 6
4034.2.i \(\chi_{4034}(765, \cdot)\) n/a 680 4
4034.2.j \(\chi_{4034}(817, \cdot)\) n/a 1020 6
4034.2.k \(\chi_{4034}(691, \cdot)\) n/a 1352 8
4034.2.l \(\chi_{4034}(1029, \cdot)\) n/a 1008 6
4034.2.m \(\chi_{4034}(899, \cdot)\) n/a 2040 12
4034.2.n \(\chi_{4034}(1701, \cdot)\) n/a 1360 8
4034.2.o \(\chi_{4034}(783, \cdot)\) n/a 2040 12
4034.2.q \(\chi_{4034}(207, \cdot)\) n/a 2016 12
4034.2.r \(\chi_{4034}(175, \cdot)\) n/a 2040 12
4034.2.s \(\chi_{4034}(77, \cdot)\) n/a 2704 16
4034.2.t \(\chi_{4034}(313, \cdot)\) n/a 4080 24
4034.2.u \(\chi_{4034}(139, \cdot)\) n/a 6048 36
4034.2.v \(\chi_{4034}(99, \cdot)\) n/a 4032 24
4034.2.w \(\chi_{4034}(75, \cdot)\) n/a 4080 24
4034.2.y \(\chi_{4034}(61, \cdot)\) n/a 8112 48
4034.2.z \(\chi_{4034}(93, \cdot)\) n/a 6048 36
4034.2.ba \(\chi_{4034}(169, \cdot)\) n/a 8016 48
4034.2.bb \(\chi_{4034}(65, \cdot)\) n/a 8160 48
4034.2.bd \(\chi_{4034}(11, \cdot)\) n/a 12096 72
4034.2.bf \(\chi_{4034}(27, \cdot)\) n/a 16224 96
4034.2.bg \(\chi_{4034}(9, \cdot)\) n/a 24192 144
4034.2.bi \(\chi_{4034}(3, \cdot)\) n/a 48096 288

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4034))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4034)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(2017))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database