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Properties

Label 2100.1
Level 2100
Weight 1
Dimension 106
Nonzero newspaces 9
Newform subspaces 25
Sturm bound 230400
Trace bound 21

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Defining parameters

Level: \( N \) = \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 9 \)
Newform subspaces: \( 25 \)
Sturm bound: \(230400\)
Trace bound: \(21\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2100))\).

Total New Old
Modular forms 3688 518 3170
Cusp forms 328 106 222
Eisenstein series 3360 412 2948

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 106 0 0 0

Trace form

\( 106 q + q^{3} + 8 q^{6} + q^{7} + 7 q^{9} + 2 q^{13} - q^{19} + 4 q^{21} + 32 q^{22} - 6 q^{24} - 8 q^{25} - 2 q^{27} + 32 q^{30} + 7 q^{31} - 16 q^{36} - 9 q^{37} - q^{39} + 2 q^{43} - 4 q^{46} + q^{49}+ \cdots - 4 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2100))\)

We only show spaces with odd 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
2100.1.b \(\chi_{2100}(799, \cdot)\) None 0 1
2100.1.e \(\chi_{2100}(449, \cdot)\) None 0 1
2100.1.g \(\chi_{2100}(701, \cdot)\) None 0 1
2100.1.h \(\chi_{2100}(1051, \cdot)\) None 0 1
2100.1.j \(\chi_{2100}(601, \cdot)\) None 0 1
2100.1.m \(\chi_{2100}(251, \cdot)\) 2100.1.m.a 1 1
2100.1.m.b 1
2100.1.m.c 1
2100.1.m.d 1
2100.1.o \(\chi_{2100}(2099, \cdot)\) None 0 1
2100.1.p \(\chi_{2100}(349, \cdot)\) None 0 1
2100.1.r \(\chi_{2100}(307, \cdot)\) None 0 2
2100.1.u \(\chi_{2100}(293, \cdot)\) 2100.1.u.a 8 2
2100.1.u.b 8
2100.1.v \(\chi_{2100}(757, \cdot)\) None 0 2
2100.1.y \(\chi_{2100}(407, \cdot)\) None 0 2
2100.1.ba \(\chi_{2100}(551, \cdot)\) 2100.1.ba.a 2 2
2100.1.ba.b 2
2100.1.ba.c 2
2100.1.ba.d 2
2100.1.bd \(\chi_{2100}(901, \cdot)\) None 0 2
2100.1.be \(\chi_{2100}(649, \cdot)\) None 0 2
2100.1.bf \(\chi_{2100}(299, \cdot)\) None 0 2
2100.1.bh \(\chi_{2100}(149, \cdot)\) 2100.1.bh.a 4 2
2100.1.bh.b 4
2100.1.bk \(\chi_{2100}(499, \cdot)\) None 0 2
2100.1.bm \(\chi_{2100}(151, \cdot)\) None 0 2
2100.1.bn \(\chi_{2100}(401, \cdot)\) 2100.1.bn.a 2 2
2100.1.bn.b 2
2100.1.bn.c 2
2100.1.bp \(\chi_{2100}(769, \cdot)\) None 0 4
2100.1.bq \(\chi_{2100}(419, \cdot)\) 2100.1.bq.a 8 4
2100.1.bq.b 8
2100.1.bs \(\chi_{2100}(671, \cdot)\) 2100.1.bs.a 4 4
2100.1.bs.b 4
2100.1.bs.c 4
2100.1.bs.d 4
2100.1.bv \(\chi_{2100}(181, \cdot)\) None 0 4
2100.1.bx \(\chi_{2100}(211, \cdot)\) None 0 4
2100.1.by \(\chi_{2100}(281, \cdot)\) None 0 4
2100.1.ca \(\chi_{2100}(29, \cdot)\) None 0 4
2100.1.cd \(\chi_{2100}(379, \cdot)\) None 0 4
2100.1.cf \(\chi_{2100}(107, \cdot)\) 2100.1.cf.a 8 4
2100.1.cf.b 8
2100.1.cg \(\chi_{2100}(193, \cdot)\) None 0 4
2100.1.cj \(\chi_{2100}(257, \cdot)\) 2100.1.cj.a 8 4
2100.1.cj.b 8
2100.1.ck \(\chi_{2100}(607, \cdot)\) None 0 4
2100.1.cn \(\chi_{2100}(323, \cdot)\) None 0 8
2100.1.cq \(\chi_{2100}(253, \cdot)\) None 0 8
2100.1.cr \(\chi_{2100}(377, \cdot)\) None 0 8
2100.1.cu \(\chi_{2100}(223, \cdot)\) None 0 8
2100.1.cw \(\chi_{2100}(221, \cdot)\) None 0 8
2100.1.cx \(\chi_{2100}(331, \cdot)\) None 0 8
2100.1.cz \(\chi_{2100}(79, \cdot)\) None 0 8
2100.1.dc \(\chi_{2100}(389, \cdot)\) None 0 8
2100.1.de \(\chi_{2100}(59, \cdot)\) None 0 8
2100.1.df \(\chi_{2100}(229, \cdot)\) None 0 8
2100.1.dg \(\chi_{2100}(61, \cdot)\) None 0 8
2100.1.dj \(\chi_{2100}(131, \cdot)\) None 0 8
2100.1.dl \(\chi_{2100}(103, \cdot)\) None 0 16
2100.1.dm \(\chi_{2100}(17, \cdot)\) None 0 16
2100.1.dp \(\chi_{2100}(37, \cdot)\) None 0 16
2100.1.dq \(\chi_{2100}(23, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2100))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2100)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 24}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(350))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(420))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(525))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(700))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1050))\)\(^{\oplus 2}\)