Properties

Label 5376.2
Level 5376
Weight 2
Dimension 316912
Nonzero newspaces 48
Sturm bound 3145728

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Defining parameters

Level: \( N \) = \( 5376 = 2^{8} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(3145728\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5376))\).

Total New Old
Modular forms 794880 318992 475888
Cusp forms 777985 316912 461073
Eisenstein series 16895 2080 14815

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5376))\)

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
5376.2.a \(\chi_{5376}(1, \cdot)\) 5376.2.a.a 1 1
5376.2.a.b 1
5376.2.a.c 1
5376.2.a.d 1
5376.2.a.e 1
5376.2.a.f 1
5376.2.a.g 1
5376.2.a.h 1
5376.2.a.i 1
5376.2.a.j 1
5376.2.a.k 1
5376.2.a.l 1
5376.2.a.m 2
5376.2.a.n 2
5376.2.a.o 2
5376.2.a.p 2
5376.2.a.q 2
5376.2.a.r 2
5376.2.a.s 2
5376.2.a.t 2
5376.2.a.u 2
5376.2.a.v 2
5376.2.a.w 2
5376.2.a.x 2
5376.2.a.y 2
5376.2.a.z 2
5376.2.a.ba 2
5376.2.a.bb 2
5376.2.a.bc 2
5376.2.a.bd 2
5376.2.a.be 2
5376.2.a.bf 2
5376.2.a.bg 3
5376.2.a.bh 3
5376.2.a.bi 3
5376.2.a.bj 3
5376.2.a.bk 4
5376.2.a.bl 4
5376.2.a.bm 4
5376.2.a.bn 4
5376.2.a.bo 4
5376.2.a.bp 4
5376.2.a.bq 4
5376.2.a.br 4
5376.2.b \(\chi_{5376}(3583, \cdot)\) n/a 128 1
5376.2.c \(\chi_{5376}(2689, \cdot)\) 5376.2.c.a 2 1
5376.2.c.b 2
5376.2.c.c 2
5376.2.c.d 2
5376.2.c.e 2
5376.2.c.f 2
5376.2.c.g 2
5376.2.c.h 2
5376.2.c.i 2
5376.2.c.j 2
5376.2.c.k 2
5376.2.c.l 2
5376.2.c.m 2
5376.2.c.n 2
5376.2.c.o 2
5376.2.c.p 2
5376.2.c.q 2
5376.2.c.r 2
5376.2.c.s 2
5376.2.c.t 2
5376.2.c.u 2
5376.2.c.v 2
5376.2.c.w 2
5376.2.c.x 2
5376.2.c.y 2
5376.2.c.z 2
5376.2.c.ba 2
5376.2.c.bb 2
5376.2.c.bc 2
5376.2.c.bd 2
5376.2.c.be 2
5376.2.c.bf 2
5376.2.c.bg 4
5376.2.c.bh 4
5376.2.c.bi 4
5376.2.c.bj 4
5376.2.c.bk 4
5376.2.c.bl 4
5376.2.c.bm 4
5376.2.c.bn 4
5376.2.h \(\chi_{5376}(4607, \cdot)\) n/a 192 1
5376.2.i \(\chi_{5376}(5249, \cdot)\) n/a 248 1
5376.2.j \(\chi_{5376}(1919, \cdot)\) n/a 192 1
5376.2.k \(\chi_{5376}(2561, \cdot)\) n/a 248 1
5376.2.p \(\chi_{5376}(895, \cdot)\) n/a 128 1
5376.2.q \(\chi_{5376}(1537, \cdot)\) n/a 256 2
5376.2.s \(\chi_{5376}(575, \cdot)\) n/a 384 2
5376.2.u \(\chi_{5376}(2239, \cdot)\) n/a 256 2
5376.2.w \(\chi_{5376}(1345, \cdot)\) n/a 192 2
5376.2.y \(\chi_{5376}(1217, \cdot)\) n/a 512 2
5376.2.bb \(\chi_{5376}(3967, \cdot)\) n/a 256 2
5376.2.bc \(\chi_{5376}(257, \cdot)\) n/a 496 2
5376.2.bd \(\chi_{5376}(3455, \cdot)\) n/a 496 2
5376.2.bi \(\chi_{5376}(2945, \cdot)\) n/a 496 2
5376.2.bj \(\chi_{5376}(767, \cdot)\) n/a 496 2
5376.2.bk \(\chi_{5376}(4225, \cdot)\) n/a 256 2
5376.2.bl \(\chi_{5376}(1279, \cdot)\) n/a 256 2
5376.2.bo \(\chi_{5376}(545, \cdot)\) n/a 992 4
5376.2.bq \(\chi_{5376}(673, \cdot)\) n/a 384 4
5376.2.bs \(\chi_{5376}(1247, \cdot)\) n/a 768 4
5376.2.bu \(\chi_{5376}(223, \cdot)\) n/a 512 4
5376.2.bw \(\chi_{5376}(1601, \cdot)\) n/a 1024 4
5376.2.by \(\chi_{5376}(193, \cdot)\) n/a 512 4
5376.2.ca \(\chi_{5376}(703, \cdot)\) n/a 512 4
5376.2.cc \(\chi_{5376}(191, \cdot)\) n/a 1024 4
5376.2.cg \(\chi_{5376}(337, \cdot)\) n/a 768 8
5376.2.ch \(\chi_{5376}(559, \cdot)\) n/a 1024 8
5376.2.ci \(\chi_{5376}(239, \cdot)\) n/a 1536 8
5376.2.cj \(\chi_{5376}(209, \cdot)\) n/a 2016 8
5376.2.cn \(\chi_{5376}(31, \cdot)\) n/a 1024 8
5376.2.cp \(\chi_{5376}(95, \cdot)\) n/a 1984 8
5376.2.cr \(\chi_{5376}(289, \cdot)\) n/a 1024 8
5376.2.ct \(\chi_{5376}(353, \cdot)\) n/a 1984 8
5376.2.cu \(\chi_{5376}(55, \cdot)\) None 0 16
5376.2.cx \(\chi_{5376}(169, \cdot)\) None 0 16
5376.2.cy \(\chi_{5376}(71, \cdot)\) None 0 16
5376.2.db \(\chi_{5376}(41, \cdot)\) None 0 16
5376.2.de \(\chi_{5376}(17, \cdot)\) n/a 4032 16
5376.2.df \(\chi_{5376}(431, \cdot)\) n/a 4032 16
5376.2.dg \(\chi_{5376}(271, \cdot)\) n/a 2048 16
5376.2.dh \(\chi_{5376}(529, \cdot)\) n/a 2048 16
5376.2.dm \(\chi_{5376}(85, \cdot)\) n/a 12288 32
5376.2.dn \(\chi_{5376}(125, \cdot)\) n/a 32640 32
5376.2.do \(\chi_{5376}(139, \cdot)\) n/a 16384 32
5376.2.dp \(\chi_{5376}(155, \cdot)\) n/a 24576 32
5376.2.dt \(\chi_{5376}(23, \cdot)\) None 0 32
5376.2.du \(\chi_{5376}(89, \cdot)\) None 0 32
5376.2.dx \(\chi_{5376}(103, \cdot)\) None 0 32
5376.2.dy \(\chi_{5376}(25, \cdot)\) None 0 32
5376.2.ea \(\chi_{5376}(5, \cdot)\) n/a 65280 64
5376.2.eb \(\chi_{5376}(37, \cdot)\) n/a 32768 64
5376.2.eg \(\chi_{5376}(11, \cdot)\) n/a 65280 64
5376.2.eh \(\chi_{5376}(19, \cdot)\) n/a 32768 64

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5376))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5376)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(256))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(336))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(384))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(448))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(672))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(768))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(896))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1344))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1792))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2688))\)\(^{\oplus 2}\)