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Properties

Label 5880.2
Level 5880
Weight 2
Dimension 334000
Nonzero newspaces 72
Sturm bound 3612672

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Defining parameters

Level: \( N \) = \( 5880 = 2^{3} \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 72 \)
Sturm bound: \(3612672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5880))\).

Total New Old
Modular forms 914688 336328 578360
Cusp forms 891649 334000 557649
Eisenstein series 23039 2328 20711

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5880))\)

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
5880.2.a \(\chi_{5880}(1, \cdot)\) 5880.2.a.a 1 1
5880.2.a.b 1
5880.2.a.c 1
5880.2.a.d 1
5880.2.a.e 1
5880.2.a.f 1
5880.2.a.g 1
5880.2.a.h 1
5880.2.a.i 1
5880.2.a.j 1
5880.2.a.k 1
5880.2.a.l 1
5880.2.a.m 1
5880.2.a.n 1
5880.2.a.o 1
5880.2.a.p 1
5880.2.a.q 1
5880.2.a.r 1
5880.2.a.s 1
5880.2.a.t 1
5880.2.a.u 1
5880.2.a.v 1
5880.2.a.w 1
5880.2.a.x 1
5880.2.a.y 1
5880.2.a.z 1
5880.2.a.ba 1
5880.2.a.bb 1
5880.2.a.bc 1
5880.2.a.bd 1
5880.2.a.be 1
5880.2.a.bf 1
5880.2.a.bg 1
5880.2.a.bh 1
5880.2.a.bi 1
5880.2.a.bj 1
5880.2.a.bk 2
5880.2.a.bl 2
5880.2.a.bm 2
5880.2.a.bn 2
5880.2.a.bo 2
5880.2.a.bp 2
5880.2.a.bq 2
5880.2.a.br 2
5880.2.a.bs 2
5880.2.a.bt 3
5880.2.a.bu 3
5880.2.a.bv 3
5880.2.a.bw 3
5880.2.a.bx 4
5880.2.a.by 4
5880.2.a.bz 4
5880.2.a.ca 4
5880.2.d \(\chi_{5880}(391, \cdot)\) None 0 1
5880.2.e \(\chi_{5880}(491, \cdot)\) n/a 656 1
5880.2.f \(\chi_{5880}(881, \cdot)\) n/a 160 1
5880.2.g \(\chi_{5880}(2941, \cdot)\) n/a 328 1
5880.2.j \(\chi_{5880}(589, \cdot)\) n/a 492 1
5880.2.k \(\chi_{5880}(4409, \cdot)\) n/a 240 1
5880.2.p \(\chi_{5880}(4019, \cdot)\) n/a 964 1
5880.2.q \(\chi_{5880}(3919, \cdot)\) None 0 1
5880.2.t \(\chi_{5880}(3529, \cdot)\) n/a 122 1
5880.2.u \(\chi_{5880}(1469, \cdot)\) n/a 944 1
5880.2.v \(\chi_{5880}(1079, \cdot)\) None 0 1
5880.2.w \(\chi_{5880}(979, \cdot)\) n/a 480 1
5880.2.z \(\chi_{5880}(3331, \cdot)\) n/a 320 1
5880.2.ba \(\chi_{5880}(3431, \cdot)\) None 0 1
5880.2.bf \(\chi_{5880}(3821, \cdot)\) n/a 640 1
5880.2.bg \(\chi_{5880}(361, \cdot)\) n/a 160 2
5880.2.bj \(\chi_{5880}(3037, \cdot)\) n/a 960 2
5880.2.bk \(\chi_{5880}(3137, \cdot)\) n/a 492 2
5880.2.bl \(\chi_{5880}(2647, \cdot)\) None 0 2
5880.2.bm \(\chi_{5880}(587, \cdot)\) n/a 1888 2
5880.2.br \(\chi_{5880}(883, \cdot)\) n/a 984 2
5880.2.bs \(\chi_{5880}(3527, \cdot)\) None 0 2
5880.2.bt \(\chi_{5880}(97, \cdot)\) n/a 240 2
5880.2.bu \(\chi_{5880}(197, \cdot)\) n/a 1928 2
5880.2.bz \(\chi_{5880}(19, \cdot)\) n/a 960 2
5880.2.ca \(\chi_{5880}(1439, \cdot)\) None 0 2
5880.2.cb \(\chi_{5880}(509, \cdot)\) n/a 1888 2
5880.2.cc \(\chi_{5880}(3889, \cdot)\) n/a 240 2
5880.2.cf \(\chi_{5880}(2861, \cdot)\) n/a 1280 2
5880.2.ck \(\chi_{5880}(3791, \cdot)\) None 0 2
5880.2.cl \(\chi_{5880}(2371, \cdot)\) n/a 640 2
5880.2.co \(\chi_{5880}(3301, \cdot)\) n/a 640 2
5880.2.cp \(\chi_{5880}(521, \cdot)\) n/a 320 2
5880.2.cq \(\chi_{5880}(851, \cdot)\) n/a 1280 2
5880.2.cr \(\chi_{5880}(31, \cdot)\) None 0 2
5880.2.cu \(\chi_{5880}(2959, \cdot)\) None 0 2
5880.2.cv \(\chi_{5880}(4379, \cdot)\) n/a 1888 2
5880.2.da \(\chi_{5880}(3449, \cdot)\) n/a 480 2
5880.2.db \(\chi_{5880}(949, \cdot)\) n/a 960 2
5880.2.dc \(\chi_{5880}(841, \cdot)\) n/a 672 6
5880.2.dd \(\chi_{5880}(557, \cdot)\) n/a 3776 4
5880.2.de \(\chi_{5880}(313, \cdot)\) n/a 480 4
5880.2.dj \(\chi_{5880}(2567, \cdot)\) None 0 4
5880.2.dk \(\chi_{5880}(67, \cdot)\) n/a 1920 4
5880.2.dl \(\chi_{5880}(227, \cdot)\) n/a 3776 4
5880.2.dm \(\chi_{5880}(3007, \cdot)\) None 0 4
5880.2.dr \(\chi_{5880}(3497, \cdot)\) n/a 960 4
5880.2.ds \(\chi_{5880}(2077, \cdot)\) n/a 1920 4
5880.2.dv \(\chi_{5880}(461, \cdot)\) n/a 5376 6
5880.2.dw \(\chi_{5880}(71, \cdot)\) None 0 6
5880.2.dx \(\chi_{5880}(811, \cdot)\) n/a 2688 6
5880.2.ea \(\chi_{5880}(139, \cdot)\) n/a 4032 6
5880.2.eb \(\chi_{5880}(239, \cdot)\) None 0 6
5880.2.eg \(\chi_{5880}(629, \cdot)\) n/a 8016 6
5880.2.eh \(\chi_{5880}(169, \cdot)\) n/a 1008 6
5880.2.ek \(\chi_{5880}(559, \cdot)\) None 0 6
5880.2.el \(\chi_{5880}(659, \cdot)\) n/a 8016 6
5880.2.em \(\chi_{5880}(209, \cdot)\) n/a 2016 6
5880.2.en \(\chi_{5880}(1429, \cdot)\) n/a 4032 6
5880.2.eq \(\chi_{5880}(421, \cdot)\) n/a 2688 6
5880.2.er \(\chi_{5880}(41, \cdot)\) n/a 1344 6
5880.2.ew \(\chi_{5880}(1331, \cdot)\) n/a 5376 6
5880.2.ex \(\chi_{5880}(1231, \cdot)\) None 0 6
5880.2.ey \(\chi_{5880}(121, \cdot)\) n/a 1344 12
5880.2.ez \(\chi_{5880}(43, \cdot)\) n/a 8064 12
5880.2.fa \(\chi_{5880}(167, \cdot)\) None 0 12
5880.2.ff \(\chi_{5880}(433, \cdot)\) n/a 2016 12
5880.2.fg \(\chi_{5880}(533, \cdot)\) n/a 16032 12
5880.2.fh \(\chi_{5880}(13, \cdot)\) n/a 8064 12
5880.2.fi \(\chi_{5880}(113, \cdot)\) n/a 4032 12
5880.2.fn \(\chi_{5880}(127, \cdot)\) None 0 12
5880.2.fo \(\chi_{5880}(83, \cdot)\) n/a 16032 12
5880.2.fr \(\chi_{5880}(109, \cdot)\) n/a 8064 12
5880.2.fs \(\chi_{5880}(89, \cdot)\) n/a 4032 12
5880.2.ft \(\chi_{5880}(179, \cdot)\) n/a 16032 12
5880.2.fu \(\chi_{5880}(199, \cdot)\) None 0 12
5880.2.fx \(\chi_{5880}(271, \cdot)\) None 0 12
5880.2.fy \(\chi_{5880}(11, \cdot)\) n/a 10752 12
5880.2.gd \(\chi_{5880}(761, \cdot)\) n/a 2688 12
5880.2.ge \(\chi_{5880}(541, \cdot)\) n/a 5376 12
5880.2.gh \(\chi_{5880}(451, \cdot)\) n/a 5376 12
5880.2.gi \(\chi_{5880}(191, \cdot)\) None 0 12
5880.2.gj \(\chi_{5880}(101, \cdot)\) n/a 10752 12
5880.2.gm \(\chi_{5880}(289, \cdot)\) n/a 2016 12
5880.2.gn \(\chi_{5880}(269, \cdot)\) n/a 16032 12
5880.2.gs \(\chi_{5880}(359, \cdot)\) None 0 12
5880.2.gt \(\chi_{5880}(859, \cdot)\) n/a 8064 12
5880.2.gw \(\chi_{5880}(467, \cdot)\) n/a 32064 24
5880.2.gx \(\chi_{5880}(247, \cdot)\) None 0 24
5880.2.gy \(\chi_{5880}(137, \cdot)\) n/a 8064 24
5880.2.gz \(\chi_{5880}(157, \cdot)\) n/a 16128 24
5880.2.he \(\chi_{5880}(53, \cdot)\) n/a 32064 24
5880.2.hf \(\chi_{5880}(73, \cdot)\) n/a 4032 24
5880.2.hg \(\chi_{5880}(47, \cdot)\) None 0 24
5880.2.hh \(\chi_{5880}(163, \cdot)\) n/a 16128 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5880))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5880)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(280))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(392))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(420))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(490))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(588))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(735))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(840))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(980))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1176))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1470))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1960))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2940))\)\(^{\oplus 2}\)