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Properties

Label 14100.2
Level 14100
Weight 2
Dimension 2131168
Nonzero newspaces 48
Sturm bound 21196800

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Defining parameters

Level: \( N \) = \( 14100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 47 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(21196800\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(14100))\).

Total New Old
Modular forms 5324960 2138544 3186416
Cusp forms 5273441 2131168 3142273
Eisenstein series 51519 7376 44143

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(14100))\)

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
14100.2.a \(\chi_{14100}(1, \cdot)\) 14100.2.a.a 1 1
14100.2.a.b 1
14100.2.a.c 1
14100.2.a.d 1
14100.2.a.e 1
14100.2.a.f 1
14100.2.a.g 1
14100.2.a.h 1
14100.2.a.i 1
14100.2.a.j 1
14100.2.a.k 1
14100.2.a.l 1
14100.2.a.m 2
14100.2.a.n 2
14100.2.a.o 3
14100.2.a.p 3
14100.2.a.q 3
14100.2.a.r 4
14100.2.a.s 5
14100.2.a.t 5
14100.2.a.u 5
14100.2.a.v 7
14100.2.a.w 7
14100.2.a.x 7
14100.2.a.y 7
14100.2.a.z 7
14100.2.a.ba 7
14100.2.a.bb 8
14100.2.a.bc 8
14100.2.a.bd 8
14100.2.a.be 8
14100.2.a.bf 13
14100.2.a.bg 13
14100.2.f \(\chi_{14100}(3949, \cdot)\) n/a 140 1
14100.2.g \(\chi_{14100}(751, \cdot)\) n/a 912 1
14100.2.h \(\chi_{14100}(2351, \cdot)\) n/a 1748 1
14100.2.i \(\chi_{14100}(7049, \cdot)\) n/a 288 1
14100.2.n \(\chi_{14100}(3101, \cdot)\) n/a 304 1
14100.2.o \(\chi_{14100}(6299, \cdot)\) n/a 1656 1
14100.2.p \(\chi_{14100}(4699, \cdot)\) n/a 864 1
14100.2.q \(\chi_{14100}(11843, \cdot)\) n/a 3440 2
14100.2.r \(\chi_{14100}(11093, \cdot)\) n/a 552 2
14100.2.s \(\chi_{14100}(8743, \cdot)\) n/a 1656 2
14100.2.t \(\chi_{14100}(9493, \cdot)\) n/a 288 2
14100.2.y \(\chi_{14100}(2821, \cdot)\) n/a 928 4
14100.2.z \(\chi_{14100}(1409, \cdot)\) n/a 1920 4
14100.2.ba \(\chi_{14100}(5171, \cdot)\) n/a 11040 4
14100.2.bb \(\chi_{14100}(3571, \cdot)\) n/a 5760 4
14100.2.bc \(\chi_{14100}(1129, \cdot)\) n/a 912 4
14100.2.bh \(\chi_{14100}(1879, \cdot)\) n/a 5760 4
14100.2.bi \(\chi_{14100}(659, \cdot)\) n/a 11040 4
14100.2.bj \(\chi_{14100}(281, \cdot)\) n/a 1920 4
14100.2.bs \(\chi_{14100}(1033, \cdot)\) n/a 1920 8
14100.2.bt \(\chi_{14100}(283, \cdot)\) n/a 11040 8
14100.2.bu \(\chi_{14100}(377, \cdot)\) n/a 3680 8
14100.2.bv \(\chi_{14100}(563, \cdot)\) n/a 22976 8
14100.2.bw \(\chi_{14100}(601, \cdot)\) n/a 3344 22
14100.2.bx \(\chi_{14100}(199, \cdot)\) n/a 19008 22
14100.2.by \(\chi_{14100}(299, \cdot)\) n/a 37840 22
14100.2.bz \(\chi_{14100}(701, \cdot)\) n/a 6688 22
14100.2.ce \(\chi_{14100}(449, \cdot)\) n/a 6336 22
14100.2.cf \(\chi_{14100}(251, \cdot)\) n/a 39864 22
14100.2.cg \(\chi_{14100}(151, \cdot)\) n/a 20064 22
14100.2.ch \(\chi_{14100}(49, \cdot)\) n/a 3168 22
14100.2.cq \(\chi_{14100}(193, \cdot)\) n/a 6336 44
14100.2.cr \(\chi_{14100}(7, \cdot)\) n/a 38016 44
14100.2.cs \(\chi_{14100}(1193, \cdot)\) n/a 12672 44
14100.2.ct \(\chi_{14100}(107, \cdot)\) n/a 75680 44
14100.2.cu \(\chi_{14100}(61, \cdot)\) n/a 21120 88
14100.2.cz \(\chi_{14100}(41, \cdot)\) n/a 42240 88
14100.2.da \(\chi_{14100}(59, \cdot)\) n/a 252736 88
14100.2.db \(\chi_{14100}(19, \cdot)\) n/a 126720 88
14100.2.dg \(\chi_{14100}(169, \cdot)\) n/a 21120 88
14100.2.dh \(\chi_{14100}(31, \cdot)\) n/a 126720 88
14100.2.di \(\chi_{14100}(71, \cdot)\) n/a 252736 88
14100.2.dj \(\chi_{14100}(29, \cdot)\) n/a 42240 88
14100.2.dk \(\chi_{14100}(23, \cdot)\) n/a 505472 176
14100.2.dl \(\chi_{14100}(17, \cdot)\) n/a 84480 176
14100.2.dm \(\chi_{14100}(103, \cdot)\) n/a 253440 176
14100.2.dn \(\chi_{14100}(13, \cdot)\) n/a 42240 176

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(14100))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(14100)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(47))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(94))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(141))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(188))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(235))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(282))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(470))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(564))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(705))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(940))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1175))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1410))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2350))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2820))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3525))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4700))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7050))\)\(^{\oplus 2}\)