Properties

Label 8027.2
Level 8027
Weight 2
Dimension 2662117
Nonzero newspaces 24
Sturm bound 10718400

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Defining parameters

Level: \( N \) = \( 8027 = 23 \cdot 349 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(10718400\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8027))\).

Total New Old
Modular forms 2687256 2676693 10563
Cusp forms 2671945 2662117 9828
Eisenstein series 15311 14576 735

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8027))\)

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
8027.2.a \(\chi_{8027}(1, \cdot)\) 8027.2.a.a 1 1
8027.2.a.b 1
8027.2.a.c 143
8027.2.a.d 149
8027.2.a.e 169
8027.2.a.f 176
8027.2.c \(\chi_{8027}(4187, \cdot)\) n/a 642 1
8027.2.e \(\chi_{8027}(2669, \cdot)\) n/a 1284 2
8027.2.g \(\chi_{8027}(1609, \cdot)\) n/a 1396 2
8027.2.i \(\chi_{8027}(576, \cdot)\) n/a 1280 2
8027.2.k \(\chi_{8027}(699, \cdot)\) n/a 6960 10
8027.2.l \(\chi_{8027}(160, \cdot)\) n/a 2792 4
8027.2.o \(\chi_{8027}(348, \cdot)\) n/a 6980 10
8027.2.q \(\chi_{8027}(415, \cdot)\) n/a 18032 28
8027.2.r \(\chi_{8027}(924, \cdot)\) n/a 13960 20
8027.2.s \(\chi_{8027}(136, \cdot)\) n/a 13960 20
8027.2.v \(\chi_{8027}(139, \cdot)\) n/a 17976 28
8027.2.y \(\chi_{8027}(123, \cdot)\) n/a 13960 20
8027.2.ba \(\chi_{8027}(116, \cdot)\) n/a 35952 56
8027.2.bb \(\chi_{8027}(321, \cdot)\) n/a 39088 56
8027.2.be \(\chi_{8027}(189, \cdot)\) n/a 27920 40
8027.2.bg \(\chi_{8027}(70, \cdot)\) n/a 35840 56
8027.2.bi \(\chi_{8027}(31, \cdot)\) n/a 195440 280
8027.2.bk \(\chi_{8027}(114, \cdot)\) n/a 78176 112
8027.2.bm \(\chi_{8027}(27, \cdot)\) n/a 195440 280
8027.2.bo \(\chi_{8027}(9, \cdot)\) n/a 390880 560
8027.2.bq \(\chi_{8027}(10, \cdot)\) n/a 390880 560
8027.2.bs \(\chi_{8027}(3, \cdot)\) n/a 390880 560
8027.2.bu \(\chi_{8027}(7, \cdot)\) n/a 781760 1120

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8027))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8027)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(349))\)\(^{\oplus 2}\)