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Properties

Label 5445.2
Level 5445
Weight 2
Dimension 742389
Nonzero newspaces 48
Sturm bound 4181760

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Defining parameters

Level: \( N \) = \( 5445 = 3^{2} \cdot 5 \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(4181760\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5445))\).

Total New Old
Modular forms 1055680 749975 305705
Cusp forms 1035201 742389 292812
Eisenstein series 20479 7586 12893

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5445))\)

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
5445.2.a \(\chi_{5445}(1, \cdot)\) 5445.2.a.a 1 1
5445.2.a.b 1
5445.2.a.c 1
5445.2.a.d 1
5445.2.a.e 1
5445.2.a.f 1
5445.2.a.g 1
5445.2.a.h 1
5445.2.a.i 1
5445.2.a.j 1
5445.2.a.k 1
5445.2.a.l 1
5445.2.a.m 2
5445.2.a.n 2
5445.2.a.o 2
5445.2.a.p 2
5445.2.a.q 2
5445.2.a.r 2
5445.2.a.s 2
5445.2.a.t 2
5445.2.a.u 2
5445.2.a.v 2
5445.2.a.w 2
5445.2.a.x 2
5445.2.a.y 2
5445.2.a.z 3
5445.2.a.ba 3
5445.2.a.bb 3
5445.2.a.bc 3
5445.2.a.bd 3
5445.2.a.be 4
5445.2.a.bf 4
5445.2.a.bg 4
5445.2.a.bh 4
5445.2.a.bi 4
5445.2.a.bj 4
5445.2.a.bk 4
5445.2.a.bl 4
5445.2.a.bm 4
5445.2.a.bn 4
5445.2.a.bo 4
5445.2.a.bp 4
5445.2.a.bq 4
5445.2.a.br 4
5445.2.a.bs 4
5445.2.a.bt 4
5445.2.a.bu 4
5445.2.a.bv 4
5445.2.a.bw 6
5445.2.a.bx 6
5445.2.a.by 6
5445.2.a.bz 6
5445.2.a.ca 8
5445.2.a.cb 8
5445.2.a.cc 8
5445.2.a.cd 8
5445.2.c \(\chi_{5445}(2179, \cdot)\) n/a 264 1
5445.2.d \(\chi_{5445}(5444, \cdot)\) n/a 216 1
5445.2.f \(\chi_{5445}(3266, \cdot)\) n/a 144 1
5445.2.i \(\chi_{5445}(1816, \cdot)\) n/a 872 2
5445.2.k \(\chi_{5445}(1693, \cdot)\) n/a 524 2
5445.2.l \(\chi_{5445}(2663, \cdot)\) n/a 436 2
5445.2.n \(\chi_{5445}(856, \cdot)\) n/a 720 4
5445.2.p \(\chi_{5445}(1451, \cdot)\) n/a 864 2
5445.2.r \(\chi_{5445}(1814, \cdot)\) n/a 1264 2
5445.2.u \(\chi_{5445}(364, \cdot)\) n/a 1272 2
5445.2.x \(\chi_{5445}(161, \cdot)\) n/a 576 4
5445.2.z \(\chi_{5445}(1304, \cdot)\) n/a 864 4
5445.2.ba \(\chi_{5445}(874, \cdot)\) n/a 1048 4
5445.2.bc \(\chi_{5445}(496, \cdot)\) n/a 2200 10
5445.2.bd \(\chi_{5445}(122, \cdot)\) n/a 2544 4
5445.2.bg \(\chi_{5445}(967, \cdot)\) n/a 2528 4
5445.2.bh \(\chi_{5445}(511, \cdot)\) n/a 3456 8
5445.2.bj \(\chi_{5445}(323, \cdot)\) n/a 1728 8
5445.2.bk \(\chi_{5445}(118, \cdot)\) n/a 2096 8
5445.2.bo \(\chi_{5445}(296, \cdot)\) n/a 1760 10
5445.2.bq \(\chi_{5445}(494, \cdot)\) n/a 2640 10
5445.2.br \(\chi_{5445}(199, \cdot)\) n/a 3280 10
5445.2.bt \(\chi_{5445}(124, \cdot)\) n/a 5056 8
5445.2.bw \(\chi_{5445}(239, \cdot)\) n/a 5056 8
5445.2.by \(\chi_{5445}(596, \cdot)\) n/a 3456 8
5445.2.ca \(\chi_{5445}(166, \cdot)\) n/a 10560 20
5445.2.cc \(\chi_{5445}(188, \cdot)\) n/a 5280 20
5445.2.cd \(\chi_{5445}(208, \cdot)\) n/a 6560 20
5445.2.cf \(\chi_{5445}(91, \cdot)\) n/a 8800 40
5445.2.cg \(\chi_{5445}(112, \cdot)\) n/a 10112 16
5445.2.cj \(\chi_{5445}(608, \cdot)\) n/a 10112 16
5445.2.ck \(\chi_{5445}(34, \cdot)\) n/a 15760 20
5445.2.cn \(\chi_{5445}(164, \cdot)\) n/a 15760 20
5445.2.cp \(\chi_{5445}(131, \cdot)\) n/a 10560 20
5445.2.cs \(\chi_{5445}(64, \cdot)\) n/a 13120 40
5445.2.ct \(\chi_{5445}(134, \cdot)\) n/a 10560 40
5445.2.cv \(\chi_{5445}(116, \cdot)\) n/a 7040 40
5445.2.cy \(\chi_{5445}(43, \cdot)\) n/a 31520 40
5445.2.db \(\chi_{5445}(23, \cdot)\) n/a 31520 40
5445.2.dc \(\chi_{5445}(16, \cdot)\) n/a 42240 80
5445.2.de \(\chi_{5445}(28, \cdot)\) n/a 26240 80
5445.2.df \(\chi_{5445}(53, \cdot)\) n/a 21120 80
5445.2.di \(\chi_{5445}(41, \cdot)\) n/a 42240 80
5445.2.dk \(\chi_{5445}(29, \cdot)\) n/a 63040 80
5445.2.dn \(\chi_{5445}(4, \cdot)\) n/a 63040 80
5445.2.do \(\chi_{5445}(38, \cdot)\) n/a 126080 160
5445.2.dr \(\chi_{5445}(7, \cdot)\) n/a 126080 160

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5445))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5445)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(495))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(605))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1089))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1815))\)\(^{\oplus 2}\)