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Properties

Label 5819.2
Level 5819
Weight 2
Dimension 1361758
Nonzero newspaces 16
Sturm bound 5586240

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Defining parameters

Level: \( N \) = \( 5819 = 11 \cdot 23^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(5586240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5819))\).

Total New Old
Modular forms 1404040 1374438 29602
Cusp forms 1389081 1361758 27323
Eisenstein series 14959 12680 2279

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5819))\)

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
5819.2.a \(\chi_{5819}(1, \cdot)\) 5819.2.a.a 1 1
5819.2.a.b 3
5819.2.a.c 3
5819.2.a.d 5
5819.2.a.e 6
5819.2.a.f 8
5819.2.a.g 8
5819.2.a.h 9
5819.2.a.i 9
5819.2.a.j 9
5819.2.a.k 9
5819.2.a.l 18
5819.2.a.m 18
5819.2.a.n 18
5819.2.a.o 18
5819.2.a.p 40
5819.2.a.q 40
5819.2.a.r 40
5819.2.a.s 40
5819.2.a.t 60
5819.2.a.u 60
5819.2.b \(\chi_{5819}(5818, \cdot)\) n/a 484 1
5819.2.e \(\chi_{5819}(1059, \cdot)\) n/a 1936 4
5819.2.h \(\chi_{5819}(1586, \cdot)\) n/a 1936 4
5819.2.i \(\chi_{5819}(177, \cdot)\) n/a 4200 10
5819.2.l \(\chi_{5819}(263, \cdot)\) n/a 4840 10
5819.2.m \(\chi_{5819}(254, \cdot)\) n/a 10120 22
5819.2.p \(\chi_{5819}(252, \cdot)\) n/a 12100 22
5819.2.q \(\chi_{5819}(170, \cdot)\) n/a 19360 40
5819.2.r \(\chi_{5819}(28, \cdot)\) n/a 19360 40
5819.2.u \(\chi_{5819}(47, \cdot)\) n/a 48400 88
5819.2.v \(\chi_{5819}(68, \cdot)\) n/a 48400 88
5819.2.y \(\chi_{5819}(12, \cdot)\) n/a 101200 220
5819.2.z \(\chi_{5819}(10, \cdot)\) n/a 121000 220
5819.2.bc \(\chi_{5819}(3, \cdot)\) n/a 484000 880
5819.2.bf \(\chi_{5819}(7, \cdot)\) n/a 484000 880

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5819))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5819)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(253))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(529))\)\(^{\oplus 2}\)