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Properties

Label 1332.1
Level 1332
Weight 1
Dimension 82
Nonzero newspaces 10
Newform subspaces 13
Sturm bound 98496
Trace bound 25

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Defining parameters

Level: \( N \) = \( 1332 = 2^{2} \cdot 3^{2} \cdot 37 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 10 \)
Newform subspaces: \( 13 \)
Sturm bound: \(98496\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1332))\).

Total New Old
Modular forms 1652 396 1256
Cusp forms 212 82 130
Eisenstein series 1440 314 1126

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 80 0 2 0

Trace form

\( 82 q + q^{2} + q^{4} + 2 q^{5} - 2 q^{7} + q^{8} + O(q^{10}) \) \( 82 q + q^{2} + q^{4} + 2 q^{5} - 2 q^{7} + q^{8} + 2 q^{10} - 2 q^{13} - 3 q^{16} + 4 q^{17} + 2 q^{19} + 2 q^{20} + 2 q^{23} - 5 q^{25} - 7 q^{26} - 8 q^{28} + 4 q^{29} + q^{32} - 6 q^{34} + 7 q^{37} - 7 q^{40} + 2 q^{41} - 2 q^{47} - 5 q^{49} - 6 q^{50} - 2 q^{52} + 2 q^{58} - 11 q^{61} + q^{64} - 5 q^{65} + 2 q^{68} + 8 q^{70} - 2 q^{71} - 6 q^{73} + q^{74} - 2 q^{79} + 2 q^{80} - 2 q^{82} + 2 q^{83} - 5 q^{85} - 5 q^{89} - 6 q^{91} - 2 q^{97} + q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1332))\)

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
1332.1.b \(\chi_{1332}(739, \cdot)\) 1332.1.b.a 1 1
1332.1.b.b 1
1332.1.b.c 2
1332.1.b.d 4
1332.1.d \(\chi_{1332}(593, \cdot)\) None 0 1
1332.1.f \(\chi_{1332}(667, \cdot)\) None 0 1
1332.1.h \(\chi_{1332}(665, \cdot)\) None 0 1
1332.1.m \(\chi_{1332}(179, \cdot)\) 1332.1.m.a 4 2
1332.1.o \(\chi_{1332}(253, \cdot)\) 1332.1.o.a 2 2
1332.1.r \(\chi_{1332}(137, \cdot)\) None 0 2
1332.1.t \(\chi_{1332}(175, \cdot)\) None 0 2
1332.1.v \(\chi_{1332}(211, \cdot)\) None 0 2
1332.1.w \(\chi_{1332}(233, \cdot)\) None 0 2
1332.1.x \(\chi_{1332}(221, \cdot)\) None 0 2
1332.1.y \(\chi_{1332}(343, \cdot)\) 1332.1.y.a 2 2
1332.1.ba \(\chi_{1332}(223, \cdot)\) None 0 2
1332.1.bc \(\chi_{1332}(101, \cdot)\) None 0 2
1332.1.be \(\chi_{1332}(619, \cdot)\) None 0 2
1332.1.bf \(\chi_{1332}(269, \cdot)\) None 0 2
1332.1.bh \(\chi_{1332}(149, \cdot)\) None 0 2
1332.1.bj \(\chi_{1332}(307, \cdot)\) 1332.1.bj.a 4 2
1332.1.bl \(\chi_{1332}(295, \cdot)\) None 0 2
1332.1.bo \(\chi_{1332}(581, \cdot)\) None 0 2
1332.1.bp \(\chi_{1332}(545, \cdot)\) None 0 2
1332.1.br \(\chi_{1332}(655, \cdot)\) None 0 2
1332.1.bw \(\chi_{1332}(563, \cdot)\) None 0 4
1332.1.bx \(\chi_{1332}(325, \cdot)\) None 0 4
1332.1.ca \(\chi_{1332}(637, \cdot)\) None 0 4
1332.1.cb \(\chi_{1332}(265, \cdot)\) None 0 4
1332.1.cd \(\chi_{1332}(251, \cdot)\) 1332.1.cd.a 8 4
1332.1.cg \(\chi_{1332}(23, \cdot)\) None 0 4
1332.1.ch \(\chi_{1332}(191, \cdot)\) None 0 4
1332.1.ck \(\chi_{1332}(97, \cdot)\) None 0 4
1332.1.cl \(\chi_{1332}(293, \cdot)\) None 0 6
1332.1.cm \(\chi_{1332}(895, \cdot)\) None 0 6
1332.1.cn \(\chi_{1332}(67, \cdot)\) None 0 6
1332.1.co \(\chi_{1332}(41, \cdot)\) None 0 6
1332.1.cv \(\chi_{1332}(485, \cdot)\) None 0 6
1332.1.cw \(\chi_{1332}(509, \cdot)\) None 0 6
1332.1.cx \(\chi_{1332}(115, \cdot)\) None 0 6
1332.1.cy \(\chi_{1332}(559, \cdot)\) 1332.1.cy.a 12 6
1332.1.cz \(\chi_{1332}(127, \cdot)\) 1332.1.cz.a 6 6
1332.1.da \(\chi_{1332}(7, \cdot)\) None 0 6
1332.1.db \(\chi_{1332}(821, \cdot)\) None 0 6
1332.1.dc \(\chi_{1332}(53, \cdot)\) None 0 6
1332.1.dg \(\chi_{1332}(167, \cdot)\) None 0 12
1332.1.dh \(\chi_{1332}(13, \cdot)\) None 0 12
1332.1.dm \(\chi_{1332}(35, \cdot)\) 1332.1.dm.a 24 12
1332.1.dn \(\chi_{1332}(109, \cdot)\) 1332.1.dn.a 12 12
1332.1.do \(\chi_{1332}(61, \cdot)\) None 0 12
1332.1.dp \(\chi_{1332}(59, \cdot)\) None 0 12

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1332))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1332)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(111))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(148))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(222))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(333))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(444))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(666))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1332))\)\(^{\oplus 1}\)