Properties

Label 6034.2
Level 6034
Weight 2
Dimension 356039
Nonzero newspaces 16
Sturm bound 4458240

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Defining parameters

Level: \( N \) = \( 6034 = 2 \cdot 7 \cdot 431 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(4458240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6034))\).

Total New Old
Modular forms 1119720 356039 763681
Cusp forms 1109401 356039 753362
Eisenstein series 10319 0 10319

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6034))\)

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
6034.2.a \(\chi_{6034}(1, \cdot)\) 6034.2.a.a 1 1
6034.2.a.b 1
6034.2.a.c 1
6034.2.a.d 1
6034.2.a.e 1
6034.2.a.f 1
6034.2.a.g 2
6034.2.a.h 2
6034.2.a.i 2
6034.2.a.j 4
6034.2.a.k 20
6034.2.a.l 20
6034.2.a.m 21
6034.2.a.n 24
6034.2.a.o 25
6034.2.a.p 27
6034.2.a.q 31
6034.2.a.r 31
6034.2.c \(\chi_{6034}(6033, \cdot)\) n/a 288 1
6034.2.e \(\chi_{6034}(863, \cdot)\) n/a 576 2
6034.2.f \(\chi_{6034}(547, \cdot)\) n/a 864 4
6034.2.i \(\chi_{6034}(3447, \cdot)\) n/a 576 2
6034.2.j \(\chi_{6034}(2491, \cdot)\) n/a 1152 4
6034.2.m \(\chi_{6034}(95, \cdot)\) n/a 2304 8
6034.2.o \(\chi_{6034}(1319, \cdot)\) n/a 2304 8
6034.2.q \(\chi_{6034}(337, \cdot)\) n/a 9072 42
6034.2.s \(\chi_{6034}(321, \cdot)\) n/a 12096 42
6034.2.u \(\chi_{6034}(9, \cdot)\) n/a 24192 84
6034.2.v \(\chi_{6034}(15, \cdot)\) n/a 36288 168
6034.2.w \(\chi_{6034}(47, \cdot)\) n/a 24192 84
6034.2.bb \(\chi_{6034}(13, \cdot)\) n/a 48384 168
6034.2.bc \(\chi_{6034}(11, \cdot)\) n/a 96768 336
6034.2.be \(\chi_{6034}(17, \cdot)\) n/a 96768 336

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6034))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6034)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(431))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(862))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3017))\)\(^{\oplus 2}\)