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Properties

Label 945.1
Level 945
Weight 1
Dimension 32
Nonzero newspaces 4
Newform subspaces 7
Sturm bound 62208
Trace bound 4

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Defining parameters

Level: \( N \) = \( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 7 \)
Sturm bound: \(62208\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(945))\).

Total New Old
Modular forms 1496 512 984
Cusp forms 56 32 24
Eisenstein series 1440 480 960

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 16 0 16 0

Trace form

\( 32 q - 6 q^{4} - 4 q^{7} - 6 q^{9} + O(q^{10}) \) \( 32 q - 6 q^{4} - 4 q^{7} - 6 q^{9} + 4 q^{10} - 8 q^{11} + 10 q^{16} + 8 q^{22} - 2 q^{25} + 4 q^{29} + 4 q^{31} - 16 q^{34} - 10 q^{35} - 6 q^{39} + 4 q^{44} - 8 q^{46} - 10 q^{49} - 4 q^{61} - 10 q^{64} + 10 q^{65} - 8 q^{67} + 4 q^{71} + 18 q^{79} - 6 q^{81} - 6 q^{84} + 30 q^{85} - 8 q^{88} - 20 q^{91} + 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(945))\)

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
945.1.c \(\chi_{945}(701, \cdot)\) None 0 1
945.1.e \(\chi_{945}(244, \cdot)\) None 0 1
945.1.f \(\chi_{945}(134, \cdot)\) None 0 1
945.1.h \(\chi_{945}(811, \cdot)\) None 0 1
945.1.n \(\chi_{945}(188, \cdot)\) 945.1.n.a 4 2
945.1.n.b 4
945.1.o \(\chi_{945}(568, \cdot)\) None 0 2
945.1.q \(\chi_{945}(334, \cdot)\) None 0 2
945.1.s \(\chi_{945}(116, \cdot)\) None 0 2
945.1.v \(\chi_{945}(179, \cdot)\) None 0 2
945.1.w \(\chi_{945}(136, \cdot)\) None 0 2
945.1.x \(\chi_{945}(181, \cdot)\) None 0 2
945.1.y \(\chi_{945}(674, \cdot)\) 945.1.y.a 8 2
945.1.ba \(\chi_{945}(449, \cdot)\) None 0 2
945.1.bc \(\chi_{945}(586, \cdot)\) None 0 2
945.1.bd \(\chi_{945}(746, \cdot)\) None 0 2
945.1.bg \(\chi_{945}(559, \cdot)\) 945.1.bg.a 2 2
945.1.bg.b 2
945.1.bi \(\chi_{945}(514, \cdot)\) None 0 2
945.1.bk \(\chi_{945}(71, \cdot)\) None 0 2
945.1.bm \(\chi_{945}(296, \cdot)\) None 0 2
945.1.bn \(\chi_{945}(19, \cdot)\) None 0 2
945.1.bp \(\chi_{945}(451, \cdot)\) None 0 2
945.1.br \(\chi_{945}(44, \cdot)\) None 0 2
945.1.bw \(\chi_{945}(37, \cdot)\) None 0 4
945.1.bx \(\chi_{945}(143, \cdot)\) None 0 4
945.1.bz \(\chi_{945}(17, \cdot)\) None 0 4
945.1.cb \(\chi_{945}(127, \cdot)\) None 0 4
945.1.cd \(\chi_{945}(163, \cdot)\) None 0 4
945.1.cg \(\chi_{945}(458, \cdot)\) None 0 4
945.1.ci \(\chi_{945}(62, \cdot)\) None 0 4
945.1.ck \(\chi_{945}(172, \cdot)\) None 0 4
945.1.cm \(\chi_{945}(166, \cdot)\) None 0 6
945.1.cn \(\chi_{945}(29, \cdot)\) None 0 6
945.1.co \(\chi_{945}(254, \cdot)\) None 0 6
945.1.cp \(\chi_{945}(76, \cdot)\) None 0 6
945.1.cr \(\chi_{945}(31, \cdot)\) None 0 6
945.1.ct \(\chi_{945}(74, \cdot)\) None 0 6
945.1.cv \(\chi_{945}(11, \cdot)\) None 0 6
945.1.cw \(\chi_{945}(34, \cdot)\) 945.1.cw.a 6 6
945.1.cw.b 6
945.1.cy \(\chi_{945}(94, \cdot)\) None 0 6
945.1.da \(\chi_{945}(176, \cdot)\) None 0 6
945.1.dc \(\chi_{945}(191, \cdot)\) None 0 6
945.1.df \(\chi_{945}(229, \cdot)\) None 0 6
945.1.dg \(\chi_{945}(58, \cdot)\) None 0 12
945.1.dj \(\chi_{945}(47, \cdot)\) None 0 12
945.1.dl \(\chi_{945}(83, \cdot)\) None 0 12
945.1.dn \(\chi_{945}(67, \cdot)\) None 0 12
945.1.dp \(\chi_{945}(22, \cdot)\) None 0 12
945.1.dq \(\chi_{945}(38, \cdot)\) None 0 12

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(945))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(945)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(135))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(189))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(315))\)\(^{\oplus 2}\)