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Properties

Label 1100.1
Level 1100
Weight 1
Dimension 29
Nonzero newspaces 5
Newform subspaces 9
Sturm bound 72000
Trace bound 5

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Defining parameters

Level: \( N \) = \( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 5 \)
Newform subspaces: \( 9 \)
Sturm bound: \(72000\)
Trace bound: \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1100))\).

Total New Old
Modular forms 1477 397 1080
Cusp forms 77 29 48
Eisenstein series 1400 368 1032

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 29 0 0 0

Trace form

\( 29 q + 3 q^{3} + 8 q^{9} + q^{11} - 4 q^{15} + 8 q^{16} + 3 q^{23} - 8 q^{25} + 8 q^{26} - 13 q^{27} - q^{31} + 3 q^{33} + 3 q^{37} + 2 q^{45} - 6 q^{47} + q^{49} - 6 q^{53} + 2 q^{55} - 8 q^{56} - 3 q^{59}+ \cdots + 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1100))\)

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
1100.1.c \(\chi_{1100}(551, \cdot)\) None 0 1
1100.1.e \(\chi_{1100}(549, \cdot)\) 1100.1.e.a 2 1
1100.1.f \(\chi_{1100}(901, \cdot)\) 1100.1.f.a 1 1
1100.1.f.b 2
1100.1.h \(\chi_{1100}(199, \cdot)\) None 0 1
1100.1.i \(\chi_{1100}(43, \cdot)\) 1100.1.i.a 2 2
1100.1.i.b 2
1100.1.i.c 2
1100.1.i.d 2
1100.1.j \(\chi_{1100}(793, \cdot)\) None 0 2
1100.1.t \(\chi_{1100}(369, \cdot)\) None 0 4
1100.1.v \(\chi_{1100}(191, \cdot)\) None 0 4
1100.1.x \(\chi_{1100}(21, \cdot)\) 1100.1.x.a 8 4
1100.1.y \(\chi_{1100}(179, \cdot)\) None 0 4
1100.1.z \(\chi_{1100}(119, \cdot)\) None 0 4
1100.1.ba \(\chi_{1100}(159, \cdot)\) None 0 4
1100.1.bb \(\chi_{1100}(399, \cdot)\) None 0 4
1100.1.bg \(\chi_{1100}(61, \cdot)\) None 0 4
1100.1.bh \(\chi_{1100}(41, \cdot)\) None 0 4
1100.1.bi \(\chi_{1100}(101, \cdot)\) None 0 4
1100.1.bj \(\chi_{1100}(481, \cdot)\) None 0 4
1100.1.bk \(\chi_{1100}(419, \cdot)\) None 0 4
1100.1.bl \(\chi_{1100}(111, \cdot)\) None 0 4
1100.1.bn \(\chi_{1100}(689, \cdot)\) None 0 4
1100.1.bo \(\chi_{1100}(149, \cdot)\) None 0 4
1100.1.bp \(\chi_{1100}(29, \cdot)\) None 0 4
1100.1.bq \(\chi_{1100}(129, \cdot)\) None 0 4
1100.1.bv \(\chi_{1100}(31, \cdot)\) None 0 4
1100.1.bw \(\chi_{1100}(291, \cdot)\) None 0 4
1100.1.bx \(\chi_{1100}(251, \cdot)\) None 0 4
1100.1.by \(\chi_{1100}(511, \cdot)\) None 0 4
1100.1.cd \(\chi_{1100}(109, \cdot)\) 1100.1.cd.a 8 4
1100.1.cf \(\chi_{1100}(59, \cdot)\) None 0 4
1100.1.cg \(\chi_{1100}(261, \cdot)\) None 0 4
1100.1.ck \(\chi_{1100}(37, \cdot)\) None 0 8
1100.1.cl \(\chi_{1100}(83, \cdot)\) None 0 8
1100.1.cm \(\chi_{1100}(113, \cdot)\) None 0 8
1100.1.cn \(\chi_{1100}(63, \cdot)\) None 0 8
1100.1.cw \(\chi_{1100}(7, \cdot)\) None 0 8
1100.1.cx \(\chi_{1100}(133, \cdot)\) None 0 8
1100.1.cy \(\chi_{1100}(433, \cdot)\) None 0 8
1100.1.cz \(\chi_{1100}(137, \cdot)\) None 0 8
1100.1.da \(\chi_{1100}(123, \cdot)\) None 0 8
1100.1.db \(\chi_{1100}(87, \cdot)\) None 0 8
1100.1.dc \(\chi_{1100}(127, \cdot)\) None 0 8
1100.1.dd \(\chi_{1100}(93, \cdot)\) None 0 8

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1100))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1100)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(220))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(275))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(550))\)\(^{\oplus 2}\)