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Properties

Label 4338.2
Level 4338
Weight 2
Dimension 137936
Nonzero newspaces 50
Sturm bound 2090880

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Defining parameters

Level: \( N \) = \( 4338 = 2 \cdot 3^{2} \cdot 241 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 50 \)
Sturm bound: \(2090880\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4338))\).

Total New Old
Modular forms 526560 137936 388624
Cusp forms 518881 137936 380945
Eisenstein series 7679 0 7679

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4338))\)

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
4338.2.a \(\chi_{4338}(1, \cdot)\) 4338.2.a.a 1 1
4338.2.a.b 1
4338.2.a.c 1
4338.2.a.d 1
4338.2.a.e 1
4338.2.a.f 1
4338.2.a.g 1
4338.2.a.h 1
4338.2.a.i 2
4338.2.a.j 2
4338.2.a.k 2
4338.2.a.l 2
4338.2.a.m 3
4338.2.a.n 3
4338.2.a.o 3
4338.2.a.p 3
4338.2.a.q 4
4338.2.a.r 4
4338.2.a.s 4
4338.2.a.t 5
4338.2.a.u 6
4338.2.a.v 7
4338.2.a.w 7
4338.2.a.x 9
4338.2.a.y 13
4338.2.a.z 13
4338.2.d \(\chi_{4338}(1927, \cdot)\) 4338.2.d.a 2 1
4338.2.d.b 2
4338.2.d.c 2
4338.2.d.d 4
4338.2.d.e 6
4338.2.d.f 8
4338.2.d.g 8
4338.2.d.h 8
4338.2.d.i 10
4338.2.d.j 10
4338.2.d.k 20
4338.2.d.l 20
4338.2.e \(\chi_{4338}(2425, \cdot)\) n/a 484 2
4338.2.f \(\chi_{4338}(1447, \cdot)\) n/a 480 2
4338.2.g \(\chi_{4338}(979, \cdot)\) n/a 484 2
4338.2.h \(\chi_{4338}(1189, \cdot)\) n/a 204 2
4338.2.i \(\chi_{4338}(2233, \cdot)\) n/a 200 2
4338.2.k \(\chi_{4338}(91, \cdot)\) n/a 400 4
4338.2.n \(\chi_{4338}(3631, \cdot)\) n/a 484 2
4338.2.o \(\chi_{4338}(481, \cdot)\) n/a 484 2
4338.2.p \(\chi_{4338}(949, \cdot)\) n/a 484 2
4338.2.w \(\chi_{4338}(739, \cdot)\) n/a 204 2
4338.2.x \(\chi_{4338}(271, \cdot)\) n/a 396 4
4338.2.z \(\chi_{4338}(1837, \cdot)\) n/a 400 4
4338.2.bc \(\chi_{4338}(181, \cdot)\) n/a 408 4
4338.2.bg \(\chi_{4338}(301, \cdot)\) n/a 968 4
4338.2.bh \(\chi_{4338}(787, \cdot)\) n/a 968 4
4338.2.bi \(\chi_{4338}(1201, \cdot)\) n/a 968 4
4338.2.bk \(\chi_{4338}(883, \cdot)\) n/a 816 8
4338.2.bl \(\chi_{4338}(1741, \cdot)\) n/a 1936 8
4338.2.bm \(\chi_{4338}(265, \cdot)\) n/a 1936 8
4338.2.bn \(\chi_{4338}(205, \cdot)\) n/a 1936 8
4338.2.bo \(\chi_{4338}(197, \cdot)\) n/a 624 8
4338.2.br \(\chi_{4338}(235, \cdot)\) n/a 800 8
4338.2.bt \(\chi_{4338}(361, \cdot)\) n/a 808 8
4338.2.bu \(\chi_{4338}(691, \cdot)\) n/a 1936 8
4338.2.bx \(\chi_{4338}(121, \cdot)\) n/a 1936 8
4338.2.by \(\chi_{4338}(211, \cdot)\) n/a 1936 8
4338.2.ca \(\chi_{4338}(217, \cdot)\) n/a 816 8
4338.2.ch \(\chi_{4338}(277, \cdot)\) n/a 1936 8
4338.2.ci \(\chi_{4338}(187, \cdot)\) n/a 1936 8
4338.2.cj \(\chi_{4338}(733, \cdot)\) n/a 1936 8
4338.2.cn \(\chi_{4338}(289, \cdot)\) n/a 1584 16
4338.2.co \(\chi_{4338}(65, \cdot)\) n/a 3872 16
4338.2.cs \(\chi_{4338}(317, \cdot)\) n/a 3872 16
4338.2.ct \(\chi_{4338}(11, \cdot)\) n/a 3872 16
4338.2.cu \(\chi_{4338}(89, \cdot)\) n/a 1312 16
4338.2.cx \(\chi_{4338}(565, \cdot)\) n/a 3872 16
4338.2.cy \(\chi_{4338}(25, \cdot)\) n/a 3872 16
4338.2.cz \(\chi_{4338}(97, \cdot)\) n/a 3872 16
4338.2.dd \(\chi_{4338}(145, \cdot)\) n/a 1632 16
4338.2.df \(\chi_{4338}(17, \cdot)\) n/a 2496 32
4338.2.dh \(\chi_{4338}(61, \cdot)\) n/a 7744 32
4338.2.di \(\chi_{4338}(49, \cdot)\) n/a 7744 32
4338.2.dl \(\chi_{4338}(67, \cdot)\) n/a 7744 32
4338.2.dm \(\chi_{4338}(253, \cdot)\) n/a 3232 32
4338.2.dp \(\chi_{4338}(35, \cdot)\) n/a 5248 64
4338.2.dq \(\chi_{4338}(131, \cdot)\) n/a 15488 64
4338.2.dr \(\chi_{4338}(23, \cdot)\) n/a 15488 64
4338.2.dv \(\chi_{4338}(95, \cdot)\) n/a 15488 64

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4338))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4338)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(241))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(482))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(723))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1446))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2169))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4338))\)\(^{\oplus 1}\)