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Properties

Label 4901.2
Level 4901
Weight 2
Dimension 974137
Nonzero newspaces 48
Sturm bound 3974880

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Defining parameters

Level: \( N \) = \( 4901 = 13^{2} \cdot 29 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(3974880\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4901))\).

Total New Old
Modular forms 1000104 985179 14925
Cusp forms 987337 974137 13200
Eisenstein series 12767 11042 1725

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4901))\)

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
4901.2.a \(\chi_{4901}(1, \cdot)\) 4901.2.a.a 1 1
4901.2.a.b 1
4901.2.a.c 1
4901.2.a.d 2
4901.2.a.e 2
4901.2.a.f 2
4901.2.a.g 2
4901.2.a.h 4
4901.2.a.i 5
4901.2.a.j 5
4901.2.a.k 7
4901.2.a.l 9
4901.2.a.m 12
4901.2.a.n 12
4901.2.a.o 12
4901.2.a.p 14
4901.2.a.q 19
4901.2.a.r 19
4901.2.a.s 26
4901.2.a.t 38
4901.2.a.u 42
4901.2.a.v 42
4901.2.a.w 42
4901.2.a.x 42
4901.2.b \(\chi_{4901}(2029, \cdot)\) n/a 376 1
4901.2.c \(\chi_{4901}(2872, \cdot)\) n/a 358 1
4901.2.d \(\chi_{4901}(4900, \cdot)\) n/a 376 1
4901.2.e \(\chi_{4901}(146, \cdot)\) n/a 720 2
4901.2.f \(\chi_{4901}(99, \cdot)\) n/a 750 2
4901.2.k \(\chi_{4901}(70, \cdot)\) n/a 750 2
4901.2.l \(\chi_{4901}(3189, \cdot)\) n/a 752 2
4901.2.m \(\chi_{4901}(1161, \cdot)\) n/a 720 2
4901.2.n \(\chi_{4901}(2174, \cdot)\) n/a 748 2
4901.2.o \(\chi_{4901}(170, \cdot)\) n/a 2262 6
4901.2.p \(\chi_{4901}(418, \cdot)\) n/a 1500 4
4901.2.u \(\chi_{4901}(249, \cdot)\) n/a 1500 4
4901.2.v \(\chi_{4901}(378, \cdot)\) n/a 5112 12
4901.2.w \(\chi_{4901}(506, \cdot)\) n/a 2256 6
4901.2.x \(\chi_{4901}(168, \cdot)\) n/a 2244 6
4901.2.y \(\chi_{4901}(846, \cdot)\) n/a 2256 6
4901.2.z \(\chi_{4901}(315, \cdot)\) n/a 4512 12
4901.2.ba \(\chi_{4901}(376, \cdot)\) n/a 5424 12
4901.2.bb \(\chi_{4901}(233, \cdot)\) n/a 5112 12
4901.2.bc \(\chi_{4901}(144, \cdot)\) n/a 5448 12
4901.2.bd \(\chi_{4901}(437, \cdot)\) n/a 4500 12
4901.2.bi \(\chi_{4901}(408, \cdot)\) n/a 4500 12
4901.2.bj \(\chi_{4901}(204, \cdot)\) n/a 10176 24
4901.2.bk \(\chi_{4901}(22, \cdot)\) n/a 4488 12
4901.2.bl \(\chi_{4901}(23, \cdot)\) n/a 4488 12
4901.2.bm \(\chi_{4901}(361, \cdot)\) n/a 4512 12
4901.2.bn \(\chi_{4901}(307, \cdot)\) n/a 10872 24
4901.2.bs \(\chi_{4901}(278, \cdot)\) n/a 10872 24
4901.2.bt \(\chi_{4901}(289, \cdot)\) n/a 10896 24
4901.2.bu \(\chi_{4901}(30, \cdot)\) n/a 10176 24
4901.2.bv \(\chi_{4901}(173, \cdot)\) n/a 10848 24
4901.2.bw \(\chi_{4901}(19, \cdot)\) n/a 9000 24
4901.2.cb \(\chi_{4901}(89, \cdot)\) n/a 9000 24
4901.2.cc \(\chi_{4901}(53, \cdot)\) n/a 32544 72
4901.2.cd \(\chi_{4901}(128, \cdot)\) n/a 21744 48
4901.2.ci \(\chi_{4901}(41, \cdot)\) n/a 21744 48
4901.2.cj \(\chi_{4901}(92, \cdot)\) n/a 32688 72
4901.2.ck \(\chi_{4901}(25, \cdot)\) n/a 32688 72
4901.2.cl \(\chi_{4901}(38, \cdot)\) n/a 32544 72
4901.2.cm \(\chi_{4901}(16, \cdot)\) n/a 65088 144
4901.2.cn \(\chi_{4901}(8, \cdot)\) n/a 65232 144
4901.2.cs \(\chi_{4901}(18, \cdot)\) n/a 65232 144
4901.2.ct \(\chi_{4901}(4, \cdot)\) n/a 65088 144
4901.2.cu \(\chi_{4901}(36, \cdot)\) n/a 65376 144
4901.2.cv \(\chi_{4901}(9, \cdot)\) n/a 65376 144
4901.2.cw \(\chi_{4901}(11, \cdot)\) n/a 130464 288
4901.2.db \(\chi_{4901}(2, \cdot)\) n/a 130464 288

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4901))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4901)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(377))\)\(^{\oplus 2}\)