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Properties

Label 4212.2
Level 4212
Weight 2
Dimension 221872
Nonzero newspaces 66
Sturm bound 1959552

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Defining parameters

Level: \( N \) = \( 4212 = 2^{2} \cdot 3^{4} \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 66 \)
Sturm bound: \(1959552\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4212))\).

Total New Old
Modular forms 496368 224336 272032
Cusp forms 483409 221872 261537
Eisenstein series 12959 2464 10495

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4212))\)

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
4212.2.a \(\chi_{4212}(1, \cdot)\) 4212.2.a.a 1 1
4212.2.a.b 1
4212.2.a.c 2
4212.2.a.d 2
4212.2.a.e 2
4212.2.a.f 4
4212.2.a.g 4
4212.2.a.h 4
4212.2.a.i 5
4212.2.a.j 5
4212.2.a.k 6
4212.2.a.l 6
4212.2.a.m 6
4212.2.b \(\chi_{4212}(649, \cdot)\) 4212.2.b.a 2 1
4212.2.b.b 2
4212.2.b.c 2
4212.2.b.d 2
4212.2.b.e 4
4212.2.b.f 4
4212.2.b.g 12
4212.2.b.h 12
4212.2.b.i 16
4212.2.c \(\chi_{4212}(3563, \cdot)\) n/a 288 1
4212.2.h \(\chi_{4212}(4211, \cdot)\) n/a 328 1
4212.2.i \(\chi_{4212}(1405, \cdot)\) 4212.2.i.a 2 2
4212.2.i.b 2
4212.2.i.c 2
4212.2.i.d 2
4212.2.i.e 2
4212.2.i.f 2
4212.2.i.g 2
4212.2.i.h 2
4212.2.i.i 2
4212.2.i.j 2
4212.2.i.k 2
4212.2.i.l 2
4212.2.i.m 4
4212.2.i.n 4
4212.2.i.o 4
4212.2.i.p 4
4212.2.i.q 4
4212.2.i.r 4
4212.2.i.s 4
4212.2.i.t 4
4212.2.i.u 4
4212.2.i.v 8
4212.2.i.w 8
4212.2.i.x 8
4212.2.i.y 12
4212.2.j \(\chi_{4212}(2161, \cdot)\) n/a 112 2
4212.2.k \(\chi_{4212}(217, \cdot)\) n/a 112 2
4212.2.l \(\chi_{4212}(1621, \cdot)\) n/a 112 2
4212.2.n \(\chi_{4212}(811, \cdot)\) n/a 656 2
4212.2.p \(\chi_{4212}(161, \cdot)\) n/a 112 2
4212.2.s \(\chi_{4212}(971, \cdot)\) n/a 656 2
4212.2.t \(\chi_{4212}(1297, \cdot)\) n/a 112 2
4212.2.w \(\chi_{4212}(1187, \cdot)\) n/a 664 2
4212.2.x \(\chi_{4212}(1403, \cdot)\) n/a 664 2
4212.2.bc \(\chi_{4212}(3455, \cdot)\) n/a 664 2
4212.2.bd \(\chi_{4212}(1511, \cdot)\) n/a 664 2
4212.2.be \(\chi_{4212}(1837, \cdot)\) n/a 112 2
4212.2.bj \(\chi_{4212}(433, \cdot)\) n/a 112 2
4212.2.bk \(\chi_{4212}(755, \cdot)\) n/a 576 2
4212.2.bl \(\chi_{4212}(2053, \cdot)\) n/a 112 2
4212.2.bm \(\chi_{4212}(107, \cdot)\) n/a 664 2
4212.2.bp \(\chi_{4212}(647, \cdot)\) n/a 656 2
4212.2.bs \(\chi_{4212}(469, \cdot)\) n/a 216 6
4212.2.bt \(\chi_{4212}(1153, \cdot)\) n/a 252 6
4212.2.bu \(\chi_{4212}(289, \cdot)\) n/a 252 6
4212.2.bv \(\chi_{4212}(1243, \cdot)\) n/a 1328 4
4212.2.by \(\chi_{4212}(1133, \cdot)\) n/a 224 4
4212.2.bz \(\chi_{4212}(2321, \cdot)\) n/a 224 4
4212.2.cc \(\chi_{4212}(917, \cdot)\) n/a 224 4
4212.2.ce \(\chi_{4212}(163, \cdot)\) n/a 1312 4
4212.2.cf \(\chi_{4212}(379, \cdot)\) n/a 1328 4
4212.2.ci \(\chi_{4212}(271, \cdot)\) n/a 1328 4
4212.2.cj \(\chi_{4212}(593, \cdot)\) n/a 224 4
4212.2.cl \(\chi_{4212}(719, \cdot)\) n/a 1488 6
4212.2.cn \(\chi_{4212}(503, \cdot)\) n/a 1488 6
4212.2.cq \(\chi_{4212}(361, \cdot)\) n/a 252 6
4212.2.cs \(\chi_{4212}(181, \cdot)\) n/a 252 6
4212.2.cw \(\chi_{4212}(35, \cdot)\) n/a 1488 6
4212.2.cx \(\chi_{4212}(467, \cdot)\) n/a 1488 6
4212.2.cz \(\chi_{4212}(287, \cdot)\) n/a 1296 6
4212.2.dc \(\chi_{4212}(179, \cdot)\) n/a 1488 6
4212.2.de \(\chi_{4212}(829, \cdot)\) n/a 252 6
4212.2.dg \(\chi_{4212}(61, \cdot)\) n/a 2268 18
4212.2.dh \(\chi_{4212}(157, \cdot)\) n/a 1944 18
4212.2.di \(\chi_{4212}(133, \cdot)\) n/a 2268 18
4212.2.dk \(\chi_{4212}(631, \cdot)\) n/a 2976 12
4212.2.dl \(\chi_{4212}(305, \cdot)\) n/a 504 12
4212.2.dn \(\chi_{4212}(125, \cdot)\) n/a 504 12
4212.2.dp \(\chi_{4212}(19, \cdot)\) n/a 2976 12
4212.2.dr \(\chi_{4212}(307, \cdot)\) n/a 2976 12
4212.2.du \(\chi_{4212}(89, \cdot)\) n/a 504 12
4212.2.dx \(\chi_{4212}(25, \cdot)\) n/a 2268 18
4212.2.dy \(\chi_{4212}(49, \cdot)\) n/a 2268 18
4212.2.ed \(\chi_{4212}(121, \cdot)\) n/a 2268 18
4212.2.ee \(\chi_{4212}(263, \cdot)\) n/a 13536 18
4212.2.ef \(\chi_{4212}(95, \cdot)\) n/a 13536 18
4212.2.ek \(\chi_{4212}(131, \cdot)\) n/a 11664 18
4212.2.el \(\chi_{4212}(191, \cdot)\) n/a 13536 18
4212.2.em \(\chi_{4212}(23, \cdot)\) n/a 13536 18
4212.2.en \(\chi_{4212}(155, \cdot)\) n/a 13536 18
4212.2.eq \(\chi_{4212}(115, \cdot)\) n/a 27072 36
4212.2.et \(\chi_{4212}(31, \cdot)\) n/a 27072 36
4212.2.eu \(\chi_{4212}(7, \cdot)\) n/a 27072 36
4212.2.ex \(\chi_{4212}(5, \cdot)\) n/a 4536 36
4212.2.ey \(\chi_{4212}(41, \cdot)\) n/a 4536 36
4212.2.fb \(\chi_{4212}(149, \cdot)\) n/a 4536 36

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4212))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4212)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(234))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(324))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(351))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(468))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(702))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1053))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1404))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2106))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4212))\)\(^{\oplus 1}\)