# Properties

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

## 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

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