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Properties

Label 4805.2
Level 4805
Weight 2
Dimension 839961
Nonzero newspaces 24
Sturm bound 3690240

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Defining parameters

Level: \( N \) = \( 4805 = 5 \cdot 31^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(3690240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4805))\).

Total New Old
Modular forms 928080 847883 80197
Cusp forms 917041 839961 77080
Eisenstein series 11039 7922 3117

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4805))\)

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
4805.2.a \(\chi_{4805}(1, \cdot)\) 4805.2.a.a 1 1
4805.2.a.b 1
4805.2.a.c 1
4805.2.a.d 1
4805.2.a.e 1
4805.2.a.f 1
4805.2.a.g 1
4805.2.a.h 2
4805.2.a.i 4
4805.2.a.j 4
4805.2.a.k 4
4805.2.a.l 4
4805.2.a.m 4
4805.2.a.n 4
4805.2.a.o 4
4805.2.a.p 6
4805.2.a.q 8
4805.2.a.r 10
4805.2.a.s 12
4805.2.a.t 12
4805.2.a.u 12
4805.2.a.v 12
4805.2.a.w 16
4805.2.a.x 20
4805.2.a.y 20
4805.2.a.z 20
4805.2.a.ba 20
4805.2.a.bb 24
4805.2.a.bc 32
4805.2.a.bd 48
4805.2.b \(\chi_{4805}(2884, \cdot)\) n/a 436 1
4805.2.e \(\chi_{4805}(521, \cdot)\) n/a 620 2
4805.2.f \(\chi_{4805}(2882, \cdot)\) n/a 872 2
4805.2.h \(\chi_{4805}(531, \cdot)\) n/a 1232 4
4805.2.j \(\chi_{4805}(439, \cdot)\) n/a 872 2
4805.2.n \(\chi_{4805}(374, \cdot)\) n/a 1744 4
4805.2.p \(\chi_{4805}(522, \cdot)\) n/a 1744 4
4805.2.q \(\chi_{4805}(816, \cdot)\) n/a 2480 8
4805.2.r \(\chi_{4805}(333, \cdot)\) n/a 3488 8
4805.2.u \(\chi_{4805}(844, \cdot)\) n/a 3488 8
4805.2.w \(\chi_{4805}(156, \cdot)\) n/a 9960 30
4805.2.y \(\chi_{4805}(117, \cdot)\) n/a 6976 16
4805.2.bb \(\chi_{4805}(94, \cdot)\) n/a 14820 30
4805.2.bc \(\chi_{4805}(36, \cdot)\) n/a 19800 60
4805.2.be \(\chi_{4805}(92, \cdot)\) n/a 29640 60
4805.2.bf \(\chi_{4805}(16, \cdot)\) n/a 39840 120
4805.2.bh \(\chi_{4805}(129, \cdot)\) n/a 29640 60
4805.2.bj \(\chi_{4805}(4, \cdot)\) n/a 59280 120
4805.2.bm \(\chi_{4805}(37, \cdot)\) n/a 59280 120
4805.2.bo \(\chi_{4805}(41, \cdot)\) n/a 79200 240
4805.2.bq \(\chi_{4805}(23, \cdot)\) n/a 118560 240
4805.2.bs \(\chi_{4805}(9, \cdot)\) n/a 118560 240
4805.2.bu \(\chi_{4805}(3, \cdot)\) n/a 237120 480

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4805))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4805)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(155))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(961))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4805))\)\(^{\oplus 1}\)