Properties

Label 4100.2
Level 4100
Weight 2
Dimension 269048
Nonzero newspaces 98
Sturm bound 2016000

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Defining parameters

Level: \( N \) = \( 4100 = 2^{2} \cdot 5^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 98 \)
Sturm bound: \(2016000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4100))\).

Total New Old
Modular forms 509600 272248 237352
Cusp forms 498401 269048 229353
Eisenstein series 11199 3200 7999

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4100))\)

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
4100.2.a \(\chi_{4100}(1, \cdot)\) 4100.2.a.a 2 1
4100.2.a.b 2
4100.2.a.c 4
4100.2.a.d 4
4100.2.a.e 4
4100.2.a.f 6
4100.2.a.g 7
4100.2.a.h 7
4100.2.a.i 7
4100.2.a.j 7
4100.2.a.k 14
4100.2.b \(\chi_{4100}(901, \cdot)\) 4100.2.b.a 2 1
4100.2.b.b 2
4100.2.b.c 4
4100.2.b.d 4
4100.2.b.e 4
4100.2.b.f 6
4100.2.b.g 8
4100.2.b.h 10
4100.2.b.i 10
4100.2.b.j 16
4100.2.d \(\chi_{4100}(1149, \cdot)\) 4100.2.d.a 4 1
4100.2.d.b 4
4100.2.d.c 8
4100.2.d.d 8
4100.2.d.e 8
4100.2.d.f 14
4100.2.d.g 14
4100.2.g \(\chi_{4100}(2049, \cdot)\) 4100.2.g.a 4 1
4100.2.g.b 4
4100.2.g.c 8
4100.2.g.d 12
4100.2.g.e 16
4100.2.g.f 20
4100.2.j \(\chi_{4100}(2943, \cdot)\) n/a 748 2
4100.2.k \(\chi_{4100}(2543, \cdot)\) n/a 720 2
4100.2.n \(\chi_{4100}(1549, \cdot)\) n/a 124 2
4100.2.p \(\chi_{4100}(401, \cdot)\) n/a 134 2
4100.2.r \(\chi_{4100}(3443, \cdot)\) n/a 748 2
4100.2.s \(\chi_{4100}(3043, \cdot)\) n/a 748 2
4100.2.u \(\chi_{4100}(141, \cdot)\) n/a 424 4
4100.2.v \(\chi_{4100}(461, \cdot)\) n/a 424 4
4100.2.w \(\chi_{4100}(221, \cdot)\) n/a 424 4
4100.2.x \(\chi_{4100}(961, \cdot)\) n/a 424 4
4100.2.y \(\chi_{4100}(821, \cdot)\) n/a 400 4
4100.2.z \(\chi_{4100}(201, \cdot)\) n/a 264 4
4100.2.bb \(\chi_{4100}(899, \cdot)\) n/a 1496 4
4100.2.bc \(\chi_{4100}(793, \cdot)\) n/a 252 4
4100.2.bd \(\chi_{4100}(957, \cdot)\) n/a 252 4
4100.2.bh \(\chi_{4100}(1151, \cdot)\) n/a 1572 4
4100.2.bj \(\chi_{4100}(549, \cdot)\) n/a 256 4
4100.2.bl \(\chi_{4100}(701, \cdot)\) n/a 264 4
4100.2.bm \(\chi_{4100}(769, \cdot)\) n/a 416 4
4100.2.bs \(\chi_{4100}(189, \cdot)\) n/a 416 4
4100.2.bt \(\chi_{4100}(209, \cdot)\) n/a 416 4
4100.2.bw \(\chi_{4100}(269, \cdot)\) n/a 416 4
4100.2.bz \(\chi_{4100}(409, \cdot)\) n/a 416 4
4100.2.cc \(\chi_{4100}(329, \cdot)\) n/a 400 4
4100.2.ce \(\chi_{4100}(81, \cdot)\) n/a 424 4
4100.2.cg \(\chi_{4100}(761, \cdot)\) n/a 424 4
4100.2.ch \(\chi_{4100}(469, \cdot)\) n/a 416 4
4100.2.ck \(\chi_{4100}(789, \cdot)\) n/a 416 4
4100.2.cl \(\chi_{4100}(2109, \cdot)\) n/a 416 4
4100.2.cn \(\chi_{4100}(441, \cdot)\) n/a 424 4
4100.2.cq \(\chi_{4100}(681, \cdot)\) n/a 424 4
4100.2.cr \(\chi_{4100}(3721, \cdot)\) n/a 424 4
4100.2.cu \(\chi_{4100}(529, \cdot)\) n/a 416 4
4100.2.cw \(\chi_{4100}(1849, \cdot)\) n/a 256 4
4100.2.cy \(\chi_{4100}(43, \cdot)\) n/a 2992 8
4100.2.db \(\chi_{4100}(583, \cdot)\) n/a 5008 8
4100.2.dc \(\chi_{4100}(103, \cdot)\) n/a 5008 8
4100.2.dg \(\chi_{4100}(203, \cdot)\) n/a 5008 8
4100.2.dh \(\chi_{4100}(923, \cdot)\) n/a 5008 8
4100.2.di \(\chi_{4100}(1023, \cdot)\) n/a 5008 8
4100.2.dk \(\chi_{4100}(107, \cdot)\) n/a 2992 8
4100.2.dm \(\chi_{4100}(1601, \cdot)\) n/a 536 8
4100.2.do \(\chi_{4100}(49, \cdot)\) n/a 496 8
4100.2.dr \(\chi_{4100}(543, \cdot)\) n/a 2992 8
4100.2.dt \(\chi_{4100}(223, \cdot)\) n/a 5008 8
4100.2.dv \(\chi_{4100}(163, \cdot)\) n/a 5008 8
4100.2.dw \(\chi_{4100}(127, \cdot)\) n/a 5008 8
4100.2.dz \(\chi_{4100}(523, \cdot)\) n/a 5008 8
4100.2.ea \(\chi_{4100}(187, \cdot)\) n/a 5008 8
4100.2.ec \(\chi_{4100}(61, \cdot)\) n/a 832 8
4100.2.ee \(\chi_{4100}(169, \cdot)\) n/a 848 8
4100.2.eh \(\chi_{4100}(689, \cdot)\) n/a 848 8
4100.2.ei \(\chi_{4100}(1221, \cdot)\) n/a 832 8
4100.2.ej \(\chi_{4100}(21, \cdot)\) n/a 832 8
4100.2.ek \(\chi_{4100}(841, \cdot)\) n/a 832 8
4100.2.eo \(\chi_{4100}(289, \cdot)\) n/a 848 8
4100.2.ep \(\chi_{4100}(989, \cdot)\) n/a 848 8
4100.2.eq \(\chi_{4100}(9, \cdot)\) n/a 848 8
4100.2.ev \(\chi_{4100}(121, \cdot)\) n/a 832 8
4100.2.ew \(\chi_{4100}(467, \cdot)\) n/a 5008 8
4100.2.ez \(\chi_{4100}(83, \cdot)\) n/a 4800 8
4100.2.fa \(\chi_{4100}(303, \cdot)\) n/a 5008 8
4100.2.fd \(\chi_{4100}(283, \cdot)\) n/a 5008 8
4100.2.fe \(\chi_{4100}(23, \cdot)\) n/a 5008 8
4100.2.fh \(\chi_{4100}(863, \cdot)\) n/a 5008 8
4100.2.fi \(\chi_{4100}(963, \cdot)\) n/a 5008 8
4100.2.fj \(\chi_{4100}(87, \cdot)\) n/a 5008 8
4100.2.fn \(\chi_{4100}(323, \cdot)\) n/a 5008 8
4100.2.fo \(\chi_{4100}(483, \cdot)\) n/a 5008 8
4100.2.fr \(\chi_{4100}(207, \cdot)\) n/a 2992 8
4100.2.ft \(\chi_{4100}(19, \cdot)\) n/a 10016 16
4100.2.fu \(\chi_{4100}(191, \cdot)\) n/a 10016 16
4100.2.fv \(\chi_{4100}(111, \cdot)\) n/a 10016 16
4100.2.fw \(\chi_{4100}(151, \cdot)\) n/a 6288 16
4100.2.fx \(\chi_{4100}(71, \cdot)\) n/a 10016 16
4100.2.fy \(\chi_{4100}(211, \cdot)\) n/a 10016 16
4100.2.ge \(\chi_{4100}(313, \cdot)\) n/a 1680 16
4100.2.gf \(\chi_{4100}(973, \cdot)\) n/a 1680 16
4100.2.gq \(\chi_{4100}(117, \cdot)\) n/a 1680 16
4100.2.gr \(\chi_{4100}(13, \cdot)\) n/a 1680 16
4100.2.gs \(\chi_{4100}(17, \cdot)\) n/a 1680 16
4100.2.gt \(\chi_{4100}(93, \cdot)\) n/a 1008 16
4100.2.gu \(\chi_{4100}(137, \cdot)\) n/a 1680 16
4100.2.gv \(\chi_{4100}(273, \cdot)\) n/a 1680 16
4100.2.gw \(\chi_{4100}(1137, \cdot)\) n/a 1680 16
4100.2.gx \(\chi_{4100}(157, \cdot)\) n/a 1008 16
4100.2.gy \(\chi_{4100}(177, \cdot)\) n/a 1680 16
4100.2.gz \(\chi_{4100}(217, \cdot)\) n/a 1680 16
4100.2.hc \(\chi_{4100}(179, \cdot)\) n/a 10016 16
4100.2.hd \(\chi_{4100}(79, \cdot)\) n/a 10016 16
4100.2.he \(\chi_{4100}(439, \cdot)\) n/a 10016 16
4100.2.hf \(\chi_{4100}(99, \cdot)\) n/a 5984 16
4100.2.hg \(\chi_{4100}(239, \cdot)\) n/a 10016 16
4100.2.hn \(\chi_{4100}(11, \cdot)\) n/a 10016 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4100))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4100)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(82))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(164))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(205))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(410))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(820))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1025))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2050))\)\(^{\oplus 2}\)