Properties

Label 8047.2
Level 8047
Weight 2
Dimension 2643387
Nonzero newspaces 30
Sturm bound 10728480

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Defining parameters

Level: \( N \) = \( 8047 = 13 \cdot 619 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(10728480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8047))\).

Total New Old
Modular forms 2689536 2656963 32573
Cusp forms 2674705 2643387 31318
Eisenstein series 14831 13576 1255

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8047))\)

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
8047.2.a \(\chi_{8047}(1, \cdot)\) 8047.2.a.a 2 1
8047.2.a.b 142
8047.2.a.c 151
8047.2.a.d 156
8047.2.a.e 168
8047.2.c \(\chi_{8047}(1858, \cdot)\) n/a 720 1
8047.2.e \(\chi_{8047}(3461, \cdot)\) n/a 1442 2
8047.2.f \(\chi_{8047}(620, \cdot)\) n/a 1444 2
8047.2.g \(\chi_{8047}(3966, \cdot)\) n/a 1240 2
8047.2.h \(\chi_{8047}(2109, \cdot)\) n/a 1442 2
8047.2.i \(\chi_{8047}(2475, \cdot)\) n/a 1440 2
8047.2.k \(\chi_{8047}(6556, \cdot)\) n/a 1442 2
8047.2.q \(\chi_{8047}(1239, \cdot)\) n/a 1440 2
8047.2.r \(\chi_{8047}(985, \cdot)\) n/a 1442 2
8047.2.u \(\chi_{8047}(5823, \cdot)\) n/a 1444 2
8047.2.w \(\chi_{8047}(5205, \cdot)\) n/a 2888 4
8047.2.ba \(\chi_{8047}(253, \cdot)\) n/a 2884 4
8047.2.bb \(\chi_{8047}(618, \cdot)\) n/a 2888 4
8047.2.bc \(\chi_{8047}(1605, \cdot)\) n/a 2884 4
8047.2.be \(\chi_{8047}(79, \cdot)\) n/a 63240 102
8047.2.bg \(\chi_{8047}(38, \cdot)\) n/a 73440 102
8047.2.bi \(\chi_{8047}(16, \cdot)\) n/a 147084 204
8047.2.bj \(\chi_{8047}(53, \cdot)\) n/a 126480 204
8047.2.bk \(\chi_{8047}(9, \cdot)\) n/a 147288 204
8047.2.bl \(\chi_{8047}(61, \cdot)\) n/a 147084 204
8047.2.bn \(\chi_{8047}(8, \cdot)\) n/a 146880 204
8047.2.bp \(\chi_{8047}(25, \cdot)\) n/a 147288 204
8047.2.bs \(\chi_{8047}(36, \cdot)\) n/a 147084 204
8047.2.bt \(\chi_{8047}(127, \cdot)\) n/a 147288 204
8047.2.bz \(\chi_{8047}(4, \cdot)\) n/a 147084 204
8047.2.cb \(\chi_{8047}(59, \cdot)\) n/a 294168 408
8047.2.cc \(\chi_{8047}(50, \cdot)\) n/a 294576 408
8047.2.cd \(\chi_{8047}(2, \cdot)\) n/a 294168 408
8047.2.ch \(\chi_{8047}(18, \cdot)\) n/a 294576 408

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8047))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8047)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(619))\)\(^{\oplus 2}\)