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Properties

Label 4176.2
Level 4176
Weight 2
Dimension 213854
Nonzero newspaces 56
Sturm bound 1935360

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Defining parameters

Level: \( N \) = \( 4176 = 2^{4} \cdot 3^{2} \cdot 29 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 56 \)
Sturm bound: \(1935360\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4176))\).

Total New Old
Modular forms 490112 216040 274072
Cusp forms 477569 213854 263715
Eisenstein series 12543 2186 10357

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4176))\)

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
4176.2.a \(\chi_{4176}(1, \cdot)\) 4176.2.a.a 1 1
4176.2.a.b 1
4176.2.a.c 1
4176.2.a.d 1
4176.2.a.e 1
4176.2.a.f 1
4176.2.a.g 1
4176.2.a.h 1
4176.2.a.i 1
4176.2.a.j 1
4176.2.a.k 1
4176.2.a.l 1
4176.2.a.m 1
4176.2.a.n 1
4176.2.a.o 1
4176.2.a.p 1
4176.2.a.q 1
4176.2.a.r 1
4176.2.a.s 1
4176.2.a.t 1
4176.2.a.u 1
4176.2.a.v 1
4176.2.a.w 1
4176.2.a.x 1
4176.2.a.y 1
4176.2.a.z 1
4176.2.a.ba 1
4176.2.a.bb 1
4176.2.a.bc 1
4176.2.a.bd 1
4176.2.a.be 1
4176.2.a.bf 1
4176.2.a.bg 1
4176.2.a.bh 1
4176.2.a.bi 1
4176.2.a.bj 1
4176.2.a.bk 1
4176.2.a.bl 2
4176.2.a.bm 2
4176.2.a.bn 2
4176.2.a.bo 2
4176.2.a.bp 2
4176.2.a.bq 2
4176.2.a.br 2
4176.2.a.bs 2
4176.2.a.bt 2
4176.2.a.bu 3
4176.2.a.bv 3
4176.2.a.bw 3
4176.2.a.bx 3
4176.2.a.by 3
4176.2.c \(\chi_{4176}(4175, \cdot)\) 4176.2.c.a 4 1
4176.2.c.b 8
4176.2.c.c 8
4176.2.c.d 40
4176.2.e \(\chi_{4176}(3887, \cdot)\) 4176.2.e.a 4 1
4176.2.e.b 4
4176.2.e.c 4
4176.2.e.d 4
4176.2.e.e 40
4176.2.f \(\chi_{4176}(2089, \cdot)\) None 0 1
4176.2.h \(\chi_{4176}(2377, \cdot)\) None 0 1
4176.2.j \(\chi_{4176}(1799, \cdot)\) None 0 1
4176.2.l \(\chi_{4176}(2087, \cdot)\) None 0 1
4176.2.o \(\chi_{4176}(289, \cdot)\) 4176.2.o.a 2 1
4176.2.o.b 2
4176.2.o.c 2
4176.2.o.d 2
4176.2.o.e 2
4176.2.o.f 2
4176.2.o.g 2
4176.2.o.h 2
4176.2.o.i 2
4176.2.o.j 2
4176.2.o.k 2
4176.2.o.l 4
4176.2.o.m 4
4176.2.o.n 4
4176.2.o.o 4
4176.2.o.p 6
4176.2.o.q 6
4176.2.o.r 8
4176.2.o.s 16
4176.2.q \(\chi_{4176}(1393, \cdot)\) n/a 336 2
4176.2.r \(\chi_{4176}(3439, \cdot)\) n/a 150 2
4176.2.u \(\chi_{4176}(2105, \cdot)\) None 0 2
4176.2.v \(\chi_{4176}(1061, \cdot)\) n/a 480 2
4176.2.x \(\chi_{4176}(1333, \cdot)\) n/a 596 2
4176.2.z \(\chi_{4176}(1045, \cdot)\) n/a 560 2
4176.2.bc \(\chi_{4176}(1781, \cdot)\) n/a 480 2
4176.2.be \(\chi_{4176}(1027, \cdot)\) n/a 596 2
4176.2.bf \(\chi_{4176}(755, \cdot)\) n/a 448 2
4176.2.bh \(\chi_{4176}(1043, \cdot)\) n/a 480 2
4176.2.bj \(\chi_{4176}(307, \cdot)\) n/a 596 2
4176.2.bm \(\chi_{4176}(1351, \cdot)\) None 0 2
4176.2.bn \(\chi_{4176}(17, \cdot)\) n/a 120 2
4176.2.bq \(\chi_{4176}(1681, \cdot)\) n/a 356 2
4176.2.bt \(\chi_{4176}(695, \cdot)\) None 0 2
4176.2.bv \(\chi_{4176}(407, \cdot)\) None 0 2
4176.2.bx \(\chi_{4176}(985, \cdot)\) None 0 2
4176.2.bz \(\chi_{4176}(697, \cdot)\) None 0 2
4176.2.ca \(\chi_{4176}(1103, \cdot)\) n/a 336 2
4176.2.cc \(\chi_{4176}(1391, \cdot)\) n/a 360 2
4176.2.ce \(\chi_{4176}(721, \cdot)\) n/a 444 6
4176.2.cg \(\chi_{4176}(1409, \cdot)\) n/a 712 4
4176.2.ch \(\chi_{4176}(679, \cdot)\) None 0 4
4176.2.cj \(\chi_{4176}(331, \cdot)\) n/a 2864 4
4176.2.cm \(\chi_{4176}(59, \cdot)\) n/a 2688 4
4176.2.co \(\chi_{4176}(347, \cdot)\) n/a 2864 4
4176.2.cq \(\chi_{4176}(1003, \cdot)\) n/a 2864 4
4176.2.cs \(\chi_{4176}(365, \cdot)\) n/a 2864 4
4176.2.cu \(\chi_{4176}(637, \cdot)\) n/a 2864 4
4176.2.cw \(\chi_{4176}(349, \cdot)\) n/a 2688 4
4176.2.cx \(\chi_{4176}(1085, \cdot)\) n/a 2864 4
4176.2.cz \(\chi_{4176}(41, \cdot)\) None 0 4
4176.2.dc \(\chi_{4176}(655, \cdot)\) n/a 720 4
4176.2.de \(\chi_{4176}(1153, \cdot)\) n/a 444 6
4176.2.dh \(\chi_{4176}(71, \cdot)\) None 0 6
4176.2.dj \(\chi_{4176}(935, \cdot)\) None 0 6
4176.2.dl \(\chi_{4176}(361, \cdot)\) None 0 6
4176.2.dn \(\chi_{4176}(1225, \cdot)\) None 0 6
4176.2.do \(\chi_{4176}(431, \cdot)\) n/a 360 6
4176.2.dq \(\chi_{4176}(863, \cdot)\) n/a 360 6
4176.2.ds \(\chi_{4176}(49, \cdot)\) n/a 2136 12
4176.2.du \(\chi_{4176}(305, \cdot)\) n/a 720 12
4176.2.dv \(\chi_{4176}(55, \cdot)\) None 0 12
4176.2.dy \(\chi_{4176}(19, \cdot)\) n/a 3576 12
4176.2.ea \(\chi_{4176}(107, \cdot)\) n/a 2880 12
4176.2.ec \(\chi_{4176}(35, \cdot)\) n/a 2880 12
4176.2.ed \(\chi_{4176}(163, \cdot)\) n/a 3576 12
4176.2.ef \(\chi_{4176}(917, \cdot)\) n/a 2880 12
4176.2.ei \(\chi_{4176}(109, \cdot)\) n/a 3576 12
4176.2.ek \(\chi_{4176}(181, \cdot)\) n/a 3576 12
4176.2.em \(\chi_{4176}(269, \cdot)\) n/a 2880 12
4176.2.en \(\chi_{4176}(89, \cdot)\) None 0 12
4176.2.eq \(\chi_{4176}(127, \cdot)\) n/a 900 12
4176.2.es \(\chi_{4176}(383, \cdot)\) n/a 2160 12
4176.2.eu \(\chi_{4176}(239, \cdot)\) n/a 2160 12
4176.2.ev \(\chi_{4176}(25, \cdot)\) None 0 12
4176.2.ex \(\chi_{4176}(121, \cdot)\) None 0 12
4176.2.ez \(\chi_{4176}(23, \cdot)\) None 0 12
4176.2.fb \(\chi_{4176}(167, \cdot)\) None 0 12
4176.2.fe \(\chi_{4176}(241, \cdot)\) n/a 2136 12
4176.2.fg \(\chi_{4176}(31, \cdot)\) n/a 4320 24
4176.2.fj \(\chi_{4176}(137, \cdot)\) None 0 24
4176.2.fl \(\chi_{4176}(101, \cdot)\) n/a 17184 24
4176.2.fm \(\chi_{4176}(13, \cdot)\) n/a 17184 24
4176.2.fo \(\chi_{4176}(277, \cdot)\) n/a 17184 24
4176.2.fq \(\chi_{4176}(77, \cdot)\) n/a 17184 24
4176.2.fs \(\chi_{4176}(43, \cdot)\) n/a 17184 24
4176.2.fu \(\chi_{4176}(83, \cdot)\) n/a 17184 24
4176.2.fw \(\chi_{4176}(299, \cdot)\) n/a 17184 24
4176.2.fz \(\chi_{4176}(619, \cdot)\) n/a 17184 24
4176.2.gb \(\chi_{4176}(247, \cdot)\) None 0 24
4176.2.gc \(\chi_{4176}(113, \cdot)\) n/a 4272 24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4176))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4176)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(174))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(232))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(261))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(348))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(464))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(522))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(696))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1044))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1392))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2088))\)\(^{\oplus 2}\)