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Properties

Label 1116.1
Level 1116
Weight 1
Dimension 30
Nonzero newspaces 5
Newform subspaces 6
Sturm bound 69120
Trace bound 4

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Defining parameters

Level: \( N \) = \( 1116 = 2^{2} \cdot 3^{2} \cdot 31 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 5 \)
Newform subspaces: \( 6 \)
Sturm bound: \(69120\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1116))\).

Total New Old
Modular forms 1319 290 1029
Cusp forms 119 30 89
Eisenstein series 1200 260 940

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 22 4 4 0

Trace form

\( 30 q - 4 q^{4} + 2 q^{5} + O(q^{10}) \) \( 30 q - 4 q^{4} + 2 q^{5} + 4 q^{13} - 2 q^{14} + 4 q^{16} + 2 q^{17} - 2 q^{19} - 2 q^{20} - 2 q^{22} - 5 q^{25} - 4 q^{31} - 4 q^{37} + 2 q^{38} + 2 q^{41} + 7 q^{43} - 10 q^{49} - 2 q^{52} - 2 q^{53} + 2 q^{56} - 4 q^{62} - 4 q^{64} - 2 q^{65} - 2 q^{68} + 8 q^{70} - 4 q^{73} + 12 q^{76} - 4 q^{77} - q^{79} + 2 q^{80} - 12 q^{82} + 4 q^{85} + 2 q^{86} + 2 q^{88} - 5 q^{91} - 9 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1116))\)

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
1116.1.b \(\chi_{1116}(1115, \cdot)\) 1116.1.b.a 4 1
1116.1.b.b 8
1116.1.d \(\chi_{1116}(125, \cdot)\) None 0 1
1116.1.f \(\chi_{1116}(559, \cdot)\) None 0 1
1116.1.h \(\chi_{1116}(433, \cdot)\) None 0 1
1116.1.o \(\chi_{1116}(491, \cdot)\) None 0 2
1116.1.q \(\chi_{1116}(5, \cdot)\) None 0 2
1116.1.r \(\chi_{1116}(409, \cdot)\) None 0 2
1116.1.s \(\chi_{1116}(61, \cdot)\) None 0 2
1116.1.t \(\chi_{1116}(37, \cdot)\) 1116.1.t.a 2 2
1116.1.u \(\chi_{1116}(211, \cdot)\) None 0 2
1116.1.x \(\chi_{1116}(811, \cdot)\) 1116.1.x.a 4 2
1116.1.y \(\chi_{1116}(187, \cdot)\) None 0 2
1116.1.ba \(\chi_{1116}(149, \cdot)\) None 0 2
1116.1.bd \(\chi_{1116}(497, \cdot)\) None 0 2
1116.1.be \(\chi_{1116}(377, \cdot)\) 1116.1.be.a 4 2
1116.1.bg \(\chi_{1116}(119, \cdot)\) None 0 2
1116.1.bj \(\chi_{1116}(719, \cdot)\) None 0 2
1116.1.bk \(\chi_{1116}(371, \cdot)\) None 0 2
1116.1.bn \(\chi_{1116}(67, \cdot)\) None 0 2
1116.1.bo \(\chi_{1116}(553, \cdot)\) None 0 2
1116.1.bq \(\chi_{1116}(233, \cdot)\) None 0 4
1116.1.bs \(\chi_{1116}(215, \cdot)\) None 0 4
1116.1.bt \(\chi_{1116}(325, \cdot)\) None 0 4
1116.1.bv \(\chi_{1116}(163, \cdot)\) None 0 4
1116.1.ca \(\chi_{1116}(41, \cdot)\) None 0 8
1116.1.cc \(\chi_{1116}(239, \cdot)\) None 0 8
1116.1.cf \(\chi_{1116}(283, \cdot)\) None 0 8
1116.1.cg \(\chi_{1116}(19, \cdot)\) None 0 8
1116.1.cj \(\chi_{1116}(355, \cdot)\) None 0 8
1116.1.ck \(\chi_{1116}(73, \cdot)\) 1116.1.ck.a 8 8
1116.1.cl \(\chi_{1116}(85, \cdot)\) None 0 8
1116.1.cm \(\chi_{1116}(229, \cdot)\) None 0 8
1116.1.co \(\chi_{1116}(23, \cdot)\) None 0 8
1116.1.cp \(\chi_{1116}(179, \cdot)\) None 0 8
1116.1.cs \(\chi_{1116}(11, \cdot)\) None 0 8
1116.1.cu \(\chi_{1116}(413, \cdot)\) None 0 8
1116.1.cv \(\chi_{1116}(101, \cdot)\) None 0 8
1116.1.cy \(\chi_{1116}(173, \cdot)\) None 0 8
1116.1.cz \(\chi_{1116}(13, \cdot)\) None 0 8
1116.1.da \(\chi_{1116}(7, \cdot)\) None 0 8

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1116))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1116)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(93))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(124))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(279))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(372))\)\(^{\oplus 2}\)