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Properties

Label 4608.2
Level 4608
Weight 2
Dimension 261648
Nonzero newspaces 28
Sturm bound 2359296

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Defining parameters

Level: \( N \) = \( 4608 = 2^{9} \cdot 3^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 28 \)
Sturm bound: \(2359296\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4608))\).

Total New Old
Modular forms 595968 263664 332304
Cusp forms 583681 261648 322033
Eisenstein series 12287 2016 10271

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4608))\)

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
4608.2.a \(\chi_{4608}(1, \cdot)\) 4608.2.a.a 2 1
4608.2.a.b 2
4608.2.a.c 2
4608.2.a.d 2
4608.2.a.e 2
4608.2.a.f 2
4608.2.a.g 2
4608.2.a.h 2
4608.2.a.i 2
4608.2.a.j 2
4608.2.a.k 2
4608.2.a.l 2
4608.2.a.m 2
4608.2.a.n 2
4608.2.a.o 2
4608.2.a.p 2
4608.2.a.q 2
4608.2.a.r 2
4608.2.a.s 4
4608.2.a.t 4
4608.2.a.u 4
4608.2.a.v 4
4608.2.a.w 4
4608.2.a.x 4
4608.2.a.y 4
4608.2.a.z 4
4608.2.a.ba 4
4608.2.a.bb 4
4608.2.a.bc 4
4608.2.c \(\chi_{4608}(4607, \cdot)\) 4608.2.c.a 2 1
4608.2.c.b 2
4608.2.c.c 2
4608.2.c.d 2
4608.2.c.e 2
4608.2.c.f 2
4608.2.c.g 2
4608.2.c.h 2
4608.2.c.i 4
4608.2.c.j 4
4608.2.c.k 4
4608.2.c.l 4
4608.2.c.m 4
4608.2.c.n 4
4608.2.c.o 4
4608.2.c.p 4
4608.2.c.q 8
4608.2.c.r 8
4608.2.d \(\chi_{4608}(2305, \cdot)\) 4608.2.d.a 2 1
4608.2.d.b 2
4608.2.d.c 4
4608.2.d.d 4
4608.2.d.e 4
4608.2.d.f 4
4608.2.d.g 4
4608.2.d.h 4
4608.2.d.i 4
4608.2.d.j 4
4608.2.d.k 4
4608.2.d.l 4
4608.2.d.m 4
4608.2.d.n 4
4608.2.d.o 4
4608.2.d.p 8
4608.2.d.q 8
4608.2.d.r 8
4608.2.f \(\chi_{4608}(2303, \cdot)\) 4608.2.f.a 2 1
4608.2.f.b 2
4608.2.f.c 2
4608.2.f.d 2
4608.2.f.e 2
4608.2.f.f 2
4608.2.f.g 2
4608.2.f.h 2
4608.2.f.i 4
4608.2.f.j 4
4608.2.f.k 4
4608.2.f.l 4
4608.2.f.m 8
4608.2.f.n 8
4608.2.f.o 8
4608.2.f.p 8
4608.2.i \(\chi_{4608}(1537, \cdot)\) n/a 384 2
4608.2.k \(\chi_{4608}(1153, \cdot)\) 4608.2.k.a 2 2
4608.2.k.b 2
4608.2.k.c 2
4608.2.k.d 2
4608.2.k.e 2
4608.2.k.f 2
4608.2.k.g 2
4608.2.k.h 2
4608.2.k.i 2
4608.2.k.j 2
4608.2.k.k 2
4608.2.k.l 2
4608.2.k.m 2
4608.2.k.n 2
4608.2.k.o 2
4608.2.k.p 2
4608.2.k.q 2
4608.2.k.r 2
4608.2.k.s 2
4608.2.k.t 2
4608.2.k.u 2
4608.2.k.v 2
4608.2.k.w 2
4608.2.k.x 2
4608.2.k.y 4
4608.2.k.z 4
4608.2.k.ba 4
4608.2.k.bb 4
4608.2.k.bc 8
4608.2.k.bd 8
4608.2.k.be 8
4608.2.k.bf 8
4608.2.k.bg 8
4608.2.k.bh 8
4608.2.k.bi 8
4608.2.k.bj 8
4608.2.k.bk 16
4608.2.k.bl 16
4608.2.l \(\chi_{4608}(1151, \cdot)\) n/a 128 2
4608.2.p \(\chi_{4608}(767, \cdot)\) n/a 384 2
4608.2.r \(\chi_{4608}(769, \cdot)\) n/a 384 2
4608.2.s \(\chi_{4608}(1535, \cdot)\) n/a 384 2
4608.2.v \(\chi_{4608}(577, \cdot)\) n/a 304 4
4608.2.w \(\chi_{4608}(575, \cdot)\) n/a 256 4
4608.2.y \(\chi_{4608}(383, \cdot)\) n/a 768 4
4608.2.bb \(\chi_{4608}(385, \cdot)\) n/a 768 4
4608.2.bd \(\chi_{4608}(289, \cdot)\) n/a 624 8
4608.2.be \(\chi_{4608}(287, \cdot)\) n/a 512 8
4608.2.bg \(\chi_{4608}(193, \cdot)\) n/a 1472 8
4608.2.bj \(\chi_{4608}(191, \cdot)\) n/a 1472 8
4608.2.bl \(\chi_{4608}(145, \cdot)\) n/a 1264 16
4608.2.bm \(\chi_{4608}(143, \cdot)\) n/a 1024 16
4608.2.bp \(\chi_{4608}(95, \cdot)\) n/a 3008 16
4608.2.bq \(\chi_{4608}(97, \cdot)\) n/a 3008 16
4608.2.bt \(\chi_{4608}(73, \cdot)\) None 0 32
4608.2.bu \(\chi_{4608}(71, \cdot)\) None 0 32
4608.2.bw \(\chi_{4608}(47, \cdot)\) n/a 6080 32
4608.2.bz \(\chi_{4608}(49, \cdot)\) n/a 6080 32
4608.2.cb \(\chi_{4608}(37, \cdot)\) n/a 20416 64
4608.2.cc \(\chi_{4608}(35, \cdot)\) n/a 16384 64
4608.2.ce \(\chi_{4608}(25, \cdot)\) None 0 64
4608.2.ch \(\chi_{4608}(23, \cdot)\) None 0 64
4608.2.cj \(\chi_{4608}(11, \cdot)\) n/a 98048 128
4608.2.ck \(\chi_{4608}(13, \cdot)\) n/a 98048 128

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4608))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4608)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 27}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 21}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(256))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(384))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(512))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(576))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(768))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1152))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1536))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2304))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4608))\)\(^{\oplus 1}\)