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Properties

Label 1155.1
Level 1155
Weight 1
Dimension 28
Nonzero newspaces 2
Newform subspaces 6
Sturm bound 92160
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 6 \)
Sturm bound: \(92160\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1155))\).

Total New Old
Modular forms 2016 564 1452
Cusp forms 96 28 68
Eisenstein series 1920 536 1384

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 28 0 0 0

Trace form

\( 28 q - 16 q^{4} - 18 q^{9} + O(q^{10}) \) \( 28 q - 16 q^{4} - 18 q^{9} - 6 q^{15} + 8 q^{16} + 4 q^{25} + 16 q^{36} - 10 q^{39} - 8 q^{49} - 10 q^{51} - 8 q^{60} + 8 q^{64} - 12 q^{70} + 18 q^{81} + 10 q^{84} + 12 q^{91} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1155))\)

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
1155.1.b \(\chi_{1155}(736, \cdot)\) None 0 1
1155.1.e \(\chi_{1155}(1154, \cdot)\) 1155.1.e.a 2 1
1155.1.e.b 2
1155.1.e.c 4
1155.1.e.d 4
1155.1.g \(\chi_{1155}(386, \cdot)\) None 0 1
1155.1.h \(\chi_{1155}(34, \cdot)\) None 0 1
1155.1.j \(\chi_{1155}(496, \cdot)\) None 0 1
1155.1.m \(\chi_{1155}(1079, \cdot)\) None 0 1
1155.1.o \(\chi_{1155}(461, \cdot)\) None 0 1
1155.1.p \(\chi_{1155}(274, \cdot)\) None 0 1
1155.1.r \(\chi_{1155}(307, \cdot)\) None 0 2
1155.1.u \(\chi_{1155}(232, \cdot)\) None 0 2
1155.1.w \(\chi_{1155}(197, \cdot)\) None 0 2
1155.1.x \(\chi_{1155}(188, \cdot)\) None 0 2
1155.1.ba \(\chi_{1155}(254, \cdot)\) None 0 2
1155.1.bd \(\chi_{1155}(166, \cdot)\) None 0 2
1155.1.be \(\chi_{1155}(109, \cdot)\) None 0 2
1155.1.bf \(\chi_{1155}(131, \cdot)\) None 0 2
1155.1.bh \(\chi_{1155}(164, \cdot)\) None 0 2
1155.1.bk \(\chi_{1155}(571, \cdot)\) None 0 2
1155.1.bm \(\chi_{1155}(199, \cdot)\) None 0 2
1155.1.bn \(\chi_{1155}(221, \cdot)\) None 0 2
1155.1.bp \(\chi_{1155}(589, \cdot)\) None 0 4
1155.1.bq \(\chi_{1155}(41, \cdot)\) None 0 4
1155.1.bs \(\chi_{1155}(344, \cdot)\) None 0 4
1155.1.bv \(\chi_{1155}(181, \cdot)\) None 0 4
1155.1.bx \(\chi_{1155}(454, \cdot)\) None 0 4
1155.1.by \(\chi_{1155}(71, \cdot)\) None 0 4
1155.1.ca \(\chi_{1155}(314, \cdot)\) 1155.1.ca.a 8 4
1155.1.ca.b 8
1155.1.cd \(\chi_{1155}(106, \cdot)\) None 0 4
1155.1.cf \(\chi_{1155}(122, \cdot)\) None 0 4
1155.1.cg \(\chi_{1155}(32, \cdot)\) None 0 4
1155.1.ci \(\chi_{1155}(67, \cdot)\) None 0 4
1155.1.cl \(\chi_{1155}(208, \cdot)\) None 0 4
1155.1.co \(\chi_{1155}(377, \cdot)\) None 0 8
1155.1.cp \(\chi_{1155}(8, \cdot)\) None 0 8
1155.1.cr \(\chi_{1155}(148, \cdot)\) None 0 8
1155.1.cu \(\chi_{1155}(13, \cdot)\) None 0 8
1155.1.cw \(\chi_{1155}(86, \cdot)\) None 0 8
1155.1.cx \(\chi_{1155}(124, \cdot)\) None 0 8
1155.1.cz \(\chi_{1155}(46, \cdot)\) None 0 8
1155.1.dc \(\chi_{1155}(194, \cdot)\) None 0 8
1155.1.de \(\chi_{1155}(101, \cdot)\) None 0 8
1155.1.df \(\chi_{1155}(79, \cdot)\) None 0 8
1155.1.dg \(\chi_{1155}(31, \cdot)\) None 0 8
1155.1.dj \(\chi_{1155}(179, \cdot)\) None 0 8
1155.1.dk \(\chi_{1155}(52, \cdot)\) None 0 16
1155.1.dn \(\chi_{1155}(37, \cdot)\) None 0 16
1155.1.dp \(\chi_{1155}(2, \cdot)\) None 0 16
1155.1.dq \(\chi_{1155}(38, \cdot)\) None 0 16

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1155))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1155)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(231))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(385))\)\(^{\oplus 2}\)