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Properties

Label 7056.2
Level 7056
Weight 2
Dimension 576956
Nonzero newspaces 80
Sturm bound 5419008

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Defining parameters

Level: \( N \) = \( 7056 = 2^{4} \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 80 \)
Sturm bound: \(5419008\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(7056))\).

Total New Old
Modular forms 1368192 580885 787307
Cusp forms 1341313 576956 764357
Eisenstein series 26879 3929 22950

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(7056))\)

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
7056.2.a \(\chi_{7056}(1, \cdot)\) 7056.2.a.a 1 1
7056.2.a.b 1
7056.2.a.c 1
7056.2.a.d 1
7056.2.a.e 1
7056.2.a.f 1
7056.2.a.g 1
7056.2.a.h 1
7056.2.a.i 1
7056.2.a.j 1
7056.2.a.k 1
7056.2.a.l 1
7056.2.a.m 1
7056.2.a.n 1
7056.2.a.o 1
7056.2.a.p 1
7056.2.a.q 1
7056.2.a.r 1
7056.2.a.s 1
7056.2.a.t 1
7056.2.a.u 1
7056.2.a.v 1
7056.2.a.w 1
7056.2.a.x 1
7056.2.a.y 1
7056.2.a.z 1
7056.2.a.ba 1
7056.2.a.bb 1
7056.2.a.bc 1
7056.2.a.bd 1
7056.2.a.be 1
7056.2.a.bf 1
7056.2.a.bg 1
7056.2.a.bh 1
7056.2.a.bi 1
7056.2.a.bj 1
7056.2.a.bk 1
7056.2.a.bl 1
7056.2.a.bm 1
7056.2.a.bn 1
7056.2.a.bo 1
7056.2.a.bp 1
7056.2.a.bq 1
7056.2.a.br 1
7056.2.a.bs 1
7056.2.a.bt 1
7056.2.a.bu 1
7056.2.a.bv 1
7056.2.a.bw 1
7056.2.a.bx 1
7056.2.a.by 1
7056.2.a.bz 1
7056.2.a.ca 1
7056.2.a.cb 1
7056.2.a.cc 1
7056.2.a.cd 1
7056.2.a.ce 2
7056.2.a.cf 2
7056.2.a.cg 2
7056.2.a.ch 2
7056.2.a.ci 2
7056.2.a.cj 2
7056.2.a.ck 2
7056.2.a.cl 2
7056.2.a.cm 2
7056.2.a.cn 2
7056.2.a.co 2
7056.2.a.cp 2
7056.2.a.cq 2
7056.2.a.cr 2
7056.2.a.cs 2
7056.2.a.ct 2
7056.2.a.cu 2
7056.2.a.cv 2
7056.2.a.cw 2
7056.2.a.cx 2
7056.2.a.cy 4
7056.2.b \(\chi_{7056}(1567, \cdot)\) 7056.2.b.a 2 1
7056.2.b.b 2
7056.2.b.c 2
7056.2.b.d 2
7056.2.b.e 2
7056.2.b.f 2
7056.2.b.g 2
7056.2.b.h 2
7056.2.b.i 2
7056.2.b.j 2
7056.2.b.k 2
7056.2.b.l 2
7056.2.b.m 2
7056.2.b.n 2
7056.2.b.o 4
7056.2.b.p 4
7056.2.b.q 4
7056.2.b.r 4
7056.2.b.s 4
7056.2.b.t 4
7056.2.b.u 4
7056.2.b.v 4
7056.2.b.w 8
7056.2.b.x 8
7056.2.b.y 8
7056.2.b.z 16
7056.2.c \(\chi_{7056}(3529, \cdot)\) None 0 1
7056.2.h \(\chi_{7056}(4607, \cdot)\) 7056.2.h.a 2 1
7056.2.h.b 2
7056.2.h.c 2
7056.2.h.d 4
7056.2.h.e 4
7056.2.h.f 4
7056.2.h.g 4
7056.2.h.h 4
7056.2.h.i 4
7056.2.h.j 4
7056.2.h.k 8
7056.2.h.l 8
7056.2.h.m 8
7056.2.h.n 12
7056.2.h.o 12
7056.2.i \(\chi_{7056}(4409, \cdot)\) None 0 1
7056.2.j \(\chi_{7056}(1079, \cdot)\) None 0 1
7056.2.k \(\chi_{7056}(881, \cdot)\) 7056.2.k.a 4 1
7056.2.k.b 4
7056.2.k.c 8
7056.2.k.d 8
7056.2.k.e 8
7056.2.k.f 8
7056.2.k.g 8
7056.2.k.h 16
7056.2.k.i 16
7056.2.p \(\chi_{7056}(5095, \cdot)\) None 0 1
7056.2.q \(\chi_{7056}(1537, \cdot)\) n/a 472 2
7056.2.r \(\chi_{7056}(2353, \cdot)\) n/a 482 2
7056.2.s \(\chi_{7056}(3313, \cdot)\) n/a 196 2
7056.2.t \(\chi_{7056}(961, \cdot)\) n/a 472 2
7056.2.v \(\chi_{7056}(2843, \cdot)\) n/a 656 2
7056.2.x \(\chi_{7056}(3331, \cdot)\) n/a 792 2
7056.2.z \(\chi_{7056}(1765, \cdot)\) n/a 810 2
7056.2.bb \(\chi_{7056}(2645, \cdot)\) n/a 640 2
7056.2.be \(\chi_{7056}(2713, \cdot)\) None 0 2
7056.2.bf \(\chi_{7056}(31, \cdot)\) n/a 480 2
7056.2.bg \(\chi_{7056}(3449, \cdot)\) None 0 2
7056.2.bh \(\chi_{7056}(3215, \cdot)\) n/a 480 2
7056.2.bm \(\chi_{7056}(391, \cdot)\) None 0 2
7056.2.bn \(\chi_{7056}(4135, \cdot)\) None 0 2
7056.2.bs \(\chi_{7056}(1207, \cdot)\) None 0 2
7056.2.bt \(\chi_{7056}(4049, \cdot)\) n/a 160 2
7056.2.bu \(\chi_{7056}(4391, \cdot)\) None 0 2
7056.2.bz \(\chi_{7056}(3431, \cdot)\) None 0 2
7056.2.ca \(\chi_{7056}(2273, \cdot)\) n/a 472 2
7056.2.cb \(\chi_{7056}(263, \cdot)\) None 0 2
7056.2.cc \(\chi_{7056}(3233, \cdot)\) n/a 472 2
7056.2.ch \(\chi_{7056}(2255, \cdot)\) n/a 492 2
7056.2.ci \(\chi_{7056}(2873, \cdot)\) None 0 2
7056.2.cj \(\chi_{7056}(3791, \cdot)\) n/a 480 2
7056.2.ck \(\chi_{7056}(2057, \cdot)\) None 0 2
7056.2.cp \(\chi_{7056}(521, \cdot)\) None 0 2
7056.2.cq \(\chi_{7056}(863, \cdot)\) n/a 160 2
7056.2.cr \(\chi_{7056}(361, \cdot)\) None 0 2
7056.2.cs \(\chi_{7056}(4735, \cdot)\) n/a 200 2
7056.2.cx \(\chi_{7056}(3919, \cdot)\) n/a 480 2
7056.2.cy \(\chi_{7056}(2137, \cdot)\) None 0 2
7056.2.cz \(\chi_{7056}(607, \cdot)\) n/a 480 2
7056.2.da \(\chi_{7056}(1177, \cdot)\) None 0 2
7056.2.df \(\chi_{7056}(1697, \cdot)\) n/a 472 2
7056.2.dg \(\chi_{7056}(2615, \cdot)\) None 0 2
7056.2.dh \(\chi_{7056}(3559, \cdot)\) None 0 2
7056.2.dk \(\chi_{7056}(1009, \cdot)\) n/a 834 6
7056.2.dl \(\chi_{7056}(979, \cdot)\) n/a 3808 4
7056.2.dn \(\chi_{7056}(491, \cdot)\) n/a 3896 4
7056.2.dp \(\chi_{7056}(949, \cdot)\) n/a 3808 4
7056.2.ds \(\chi_{7056}(509, \cdot)\) n/a 3808 4
7056.2.dt \(\chi_{7056}(2285, \cdot)\) n/a 1280 4
7056.2.dv \(\chi_{7056}(1549, \cdot)\) n/a 1584 4
7056.2.dy \(\chi_{7056}(373, \cdot)\) n/a 3808 4
7056.2.dz \(\chi_{7056}(1685, \cdot)\) n/a 3808 4
7056.2.eb \(\chi_{7056}(851, \cdot)\) n/a 3808 4
7056.2.ed \(\chi_{7056}(19, \cdot)\) n/a 1584 4
7056.2.eg \(\chi_{7056}(619, \cdot)\) n/a 3808 4
7056.2.ei \(\chi_{7056}(275, \cdot)\) n/a 3808 4
7056.2.ej \(\chi_{7056}(2627, \cdot)\) n/a 1280 4
7056.2.el \(\chi_{7056}(1195, \cdot)\) n/a 3808 4
7056.2.en \(\chi_{7056}(293, \cdot)\) n/a 3808 4
7056.2.ep \(\chi_{7056}(589, \cdot)\) n/a 3896 4
7056.2.er \(\chi_{7056}(55, \cdot)\) None 0 6
7056.2.ew \(\chi_{7056}(1889, \cdot)\) n/a 672 6
7056.2.ex \(\chi_{7056}(71, \cdot)\) None 0 6
7056.2.ey \(\chi_{7056}(377, \cdot)\) None 0 6
7056.2.ez \(\chi_{7056}(575, \cdot)\) n/a 672 6
7056.2.fe \(\chi_{7056}(505, \cdot)\) None 0 6
7056.2.ff \(\chi_{7056}(559, \cdot)\) n/a 840 6
7056.2.fg \(\chi_{7056}(193, \cdot)\) n/a 4008 12
7056.2.fh \(\chi_{7056}(289, \cdot)\) n/a 1668 12
7056.2.fi \(\chi_{7056}(337, \cdot)\) n/a 4008 12
7056.2.fj \(\chi_{7056}(529, \cdot)\) n/a 4008 12
7056.2.fk \(\chi_{7056}(125, \cdot)\) n/a 5376 12
7056.2.fm \(\chi_{7056}(253, \cdot)\) n/a 6696 12
7056.2.fo \(\chi_{7056}(307, \cdot)\) n/a 6696 12
7056.2.fq \(\chi_{7056}(323, \cdot)\) n/a 5376 12
7056.2.fu \(\chi_{7056}(439, \cdot)\) None 0 12
7056.2.fv \(\chi_{7056}(599, \cdot)\) None 0 12
7056.2.fw \(\chi_{7056}(689, \cdot)\) n/a 4008 12
7056.2.gb \(\chi_{7056}(169, \cdot)\) None 0 12
7056.2.gc \(\chi_{7056}(367, \cdot)\) n/a 4032 12
7056.2.gd \(\chi_{7056}(25, \cdot)\) None 0 12
7056.2.ge \(\chi_{7056}(223, \cdot)\) n/a 4032 12
7056.2.gj \(\chi_{7056}(271, \cdot)\) n/a 1680 12
7056.2.gk \(\chi_{7056}(793, \cdot)\) None 0 12
7056.2.gl \(\chi_{7056}(431, \cdot)\) n/a 1344 12
7056.2.gm \(\chi_{7056}(89, \cdot)\) None 0 12
7056.2.gr \(\chi_{7056}(41, \cdot)\) None 0 12
7056.2.gs \(\chi_{7056}(527, \cdot)\) n/a 4032 12
7056.2.gt \(\chi_{7056}(761, \cdot)\) None 0 12
7056.2.gu \(\chi_{7056}(239, \cdot)\) n/a 4032 12
7056.2.gz \(\chi_{7056}(209, \cdot)\) n/a 4008 12
7056.2.ha \(\chi_{7056}(23, \cdot)\) None 0 12
7056.2.hb \(\chi_{7056}(257, \cdot)\) n/a 4008 12
7056.2.hc \(\chi_{7056}(407, \cdot)\) None 0 12
7056.2.hh \(\chi_{7056}(359, \cdot)\) None 0 12
7056.2.hi \(\chi_{7056}(17, \cdot)\) n/a 1344 12
7056.2.hj \(\chi_{7056}(199, \cdot)\) None 0 12
7056.2.ho \(\chi_{7056}(103, \cdot)\) None 0 12
7056.2.hp \(\chi_{7056}(727, \cdot)\) None 0 12
7056.2.hu \(\chi_{7056}(95, \cdot)\) n/a 4032 12
7056.2.hv \(\chi_{7056}(185, \cdot)\) None 0 12
7056.2.hw \(\chi_{7056}(943, \cdot)\) n/a 4032 12
7056.2.hx \(\chi_{7056}(457, \cdot)\) None 0 12
7056.2.ib \(\chi_{7056}(85, \cdot)\) n/a 32160 24
7056.2.id \(\chi_{7056}(461, \cdot)\) n/a 32160 24
7056.2.if \(\chi_{7056}(187, \cdot)\) n/a 32160 24
7056.2.ig \(\chi_{7056}(11, \cdot)\) n/a 32160 24
7056.2.ij \(\chi_{7056}(107, \cdot)\) n/a 10752 24
7056.2.il \(\chi_{7056}(451, \cdot)\) n/a 13392 24
7056.2.im \(\chi_{7056}(115, \cdot)\) n/a 32160 24
7056.2.ip \(\chi_{7056}(347, \cdot)\) n/a 32160 24
7056.2.ir \(\chi_{7056}(173, \cdot)\) n/a 32160 24
7056.2.it \(\chi_{7056}(37, \cdot)\) n/a 13392 24
7056.2.iu \(\chi_{7056}(277, \cdot)\) n/a 32160 24
7056.2.iw \(\chi_{7056}(5, \cdot)\) n/a 32160 24
7056.2.iz \(\chi_{7056}(269, \cdot)\) n/a 10752 24
7056.2.jb \(\chi_{7056}(205, \cdot)\) n/a 32160 24
7056.2.jd \(\chi_{7056}(155, \cdot)\) n/a 32160 24
7056.2.jf \(\chi_{7056}(139, \cdot)\) n/a 32160 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(7056))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(7056)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 45}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 27}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(294))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(336))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(392))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(441))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(504))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(588))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(784))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(882))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1008))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1176))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1764))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2352))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3528))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7056))\)\(^{\oplus 1}\)