Properties

Label 4864.2
Level 4864
Weight 2
Dimension 410648
Nonzero newspaces 36
Sturm bound 2949120

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Defining parameters

Level: \( N \) = \( 4864 = 2^{8} \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 36 \)
Sturm bound: \(2949120\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4864))\).

Total New Old
Modular forms 743616 414184 329432
Cusp forms 730945 410648 320297
Eisenstein series 12671 3536 9135

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4864))\)

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
4864.2.a \(\chi_{4864}(1, \cdot)\) 4864.2.a.a 1 1
4864.2.a.b 1
4864.2.a.c 1
4864.2.a.d 1
4864.2.a.e 1
4864.2.a.f 1
4864.2.a.g 1
4864.2.a.h 1
4864.2.a.i 1
4864.2.a.j 1
4864.2.a.k 1
4864.2.a.l 1
4864.2.a.m 1
4864.2.a.n 1
4864.2.a.o 1
4864.2.a.p 1
4864.2.a.q 2
4864.2.a.r 2
4864.2.a.s 2
4864.2.a.t 2
4864.2.a.u 2
4864.2.a.v 2
4864.2.a.w 2
4864.2.a.x 2
4864.2.a.y 2
4864.2.a.z 2
4864.2.a.ba 3
4864.2.a.bb 3
4864.2.a.bc 3
4864.2.a.bd 3
4864.2.a.be 3
4864.2.a.bf 3
4864.2.a.bg 3
4864.2.a.bh 3
4864.2.a.bi 4
4864.2.a.bj 4
4864.2.a.bk 4
4864.2.a.bl 4
4864.2.a.bm 8
4864.2.a.bn 8
4864.2.a.bo 8
4864.2.a.bp 8
4864.2.a.bq 8
4864.2.a.br 8
4864.2.a.bs 10
4864.2.a.bt 10
4864.2.b \(\chi_{4864}(2431, \cdot)\) n/a 156 1
4864.2.c \(\chi_{4864}(2433, \cdot)\) n/a 144 1
4864.2.h \(\chi_{4864}(4863, \cdot)\) n/a 156 1
4864.2.i \(\chi_{4864}(1793, \cdot)\) n/a 312 2
4864.2.k \(\chi_{4864}(1217, \cdot)\) n/a 288 2
4864.2.m \(\chi_{4864}(1215, \cdot)\) n/a 320 2
4864.2.n \(\chi_{4864}(255, \cdot)\) n/a 312 2
4864.2.s \(\chi_{4864}(639, \cdot)\) n/a 312 2
4864.2.t \(\chi_{4864}(2177, \cdot)\) n/a 312 2
4864.2.u \(\chi_{4864}(607, \cdot)\) n/a 624 4
4864.2.v \(\chi_{4864}(609, \cdot)\) n/a 576 4
4864.2.y \(\chi_{4864}(769, \cdot)\) n/a 936 6
4864.2.z \(\chi_{4864}(577, \cdot)\) n/a 640 4
4864.2.bb \(\chi_{4864}(1471, \cdot)\) n/a 640 4
4864.2.bd \(\chi_{4864}(305, \cdot)\) n/a 1152 8
4864.2.be \(\chi_{4864}(303, \cdot)\) n/a 1264 8
4864.2.bj \(\chi_{4864}(385, \cdot)\) n/a 936 6
4864.2.bl \(\chi_{4864}(127, \cdot)\) n/a 936 6
4864.2.bm \(\chi_{4864}(1535, \cdot)\) n/a 936 6
4864.2.bq \(\chi_{4864}(353, \cdot)\) n/a 1248 8
4864.2.br \(\chi_{4864}(31, \cdot)\) n/a 1248 8
4864.2.bs \(\chi_{4864}(153, \cdot)\) None 0 16
4864.2.bv \(\chi_{4864}(151, \cdot)\) None 0 16
4864.2.bw \(\chi_{4864}(319, \cdot)\) n/a 1920 12
4864.2.by \(\chi_{4864}(321, \cdot)\) n/a 1920 12
4864.2.ca \(\chi_{4864}(335, \cdot)\) n/a 2528 16
4864.2.cb \(\chi_{4864}(49, \cdot)\) n/a 2528 16
4864.2.ce \(\chi_{4864}(77, \cdot)\) n/a 18432 32
4864.2.cf \(\chi_{4864}(75, \cdot)\) n/a 20416 32
4864.2.ci \(\chi_{4864}(161, \cdot)\) n/a 3744 24
4864.2.cj \(\chi_{4864}(223, \cdot)\) n/a 3744 24
4864.2.cn \(\chi_{4864}(103, \cdot)\) None 0 32
4864.2.co \(\chi_{4864}(121, \cdot)\) None 0 32
4864.2.cs \(\chi_{4864}(17, \cdot)\) n/a 7584 48
4864.2.ct \(\chi_{4864}(15, \cdot)\) n/a 7584 48
4864.2.cw \(\chi_{4864}(27, \cdot)\) n/a 40832 64
4864.2.cx \(\chi_{4864}(45, \cdot)\) n/a 40832 64
4864.2.cz \(\chi_{4864}(71, \cdot)\) None 0 96
4864.2.da \(\chi_{4864}(9, \cdot)\) None 0 96
4864.2.dc \(\chi_{4864}(5, \cdot)\) n/a 122496 192
4864.2.dd \(\chi_{4864}(3, \cdot)\) n/a 122496 192

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4864))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4864)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(256))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(304))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(608))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1216))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2432))\)\(^{\oplus 2}\)