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Properties

Label 1740.1
Level 1740
Weight 1
Dimension 84
Nonzero newspaces 4
Newform subspaces 12
Sturm bound 161280
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1740 = 2^{2} \cdot 3 \cdot 5 \cdot 29 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 12 \)
Sturm bound: \(161280\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1740))\).

Total New Old
Modular forms 2548 404 2144
Cusp forms 308 84 224
Eisenstein series 2240 320 1920

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 84 0 0 0

Trace form

\( 84 q + 4 q^{9} + O(q^{10}) \) \( 84 q + 4 q^{9} - 24 q^{16} - 28 q^{24} + 4 q^{25} + 12 q^{33} - 28 q^{36} + 4 q^{49} - 12 q^{78} + 4 q^{81} - 12 q^{93} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1740))\)

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
1740.1.c \(\chi_{1740}(929, \cdot)\) None 0 1
1740.1.d \(\chi_{1740}(871, \cdot)\) None 0 1
1740.1.f \(\chi_{1740}(869, \cdot)\) 1740.1.f.a 1 1
1740.1.f.b 1
1740.1.f.c 1
1740.1.f.d 1
1740.1.i \(\chi_{1740}(811, \cdot)\) None 0 1
1740.1.j \(\chi_{1740}(1219, \cdot)\) None 0 1
1740.1.m \(\chi_{1740}(581, \cdot)\) None 0 1
1740.1.o \(\chi_{1740}(1159, \cdot)\) None 0 1
1740.1.p \(\chi_{1740}(521, \cdot)\) None 0 1
1740.1.r \(\chi_{1740}(191, \cdot)\) None 0 2
1740.1.s \(\chi_{1740}(829, \cdot)\) None 0 2
1740.1.v \(\chi_{1740}(347, \cdot)\) 1740.1.v.a 4 2
1740.1.v.b 4
1740.1.v.c 8
1740.1.v.d 8
1740.1.w \(\chi_{1740}(637, \cdot)\) None 0 2
1740.1.y \(\chi_{1740}(17, \cdot)\) None 0 2
1740.1.ba \(\chi_{1740}(1003, \cdot)\) None 0 2
1740.1.bd \(\chi_{1740}(307, \cdot)\) None 0 2
1740.1.bf \(\chi_{1740}(713, \cdot)\) None 0 2
1740.1.bh \(\chi_{1740}(697, \cdot)\) None 0 2
1740.1.bi \(\chi_{1740}(407, \cdot)\) None 0 2
1740.1.bl \(\chi_{1740}(481, \cdot)\) None 0 2
1740.1.bm \(\chi_{1740}(539, \cdot)\) 1740.1.bm.a 4 2
1740.1.bm.b 4
1740.1.bp \(\chi_{1740}(341, \cdot)\) None 0 6
1740.1.bq \(\chi_{1740}(439, \cdot)\) None 0 6
1740.1.bs \(\chi_{1740}(161, \cdot)\) None 0 6
1740.1.bv \(\chi_{1740}(139, \cdot)\) None 0 6
1740.1.bw \(\chi_{1740}(91, \cdot)\) None 0 6
1740.1.bz \(\chi_{1740}(149, \cdot)\) None 0 6
1740.1.cb \(\chi_{1740}(451, \cdot)\) None 0 6
1740.1.cc \(\chi_{1740}(509, \cdot)\) None 0 6
1740.1.cf \(\chi_{1740}(119, \cdot)\) 1740.1.cf.a 24 12
1740.1.cf.b 24
1740.1.cg \(\chi_{1740}(61, \cdot)\) None 0 12
1740.1.ci \(\chi_{1740}(23, \cdot)\) None 0 12
1740.1.cl \(\chi_{1740}(277, \cdot)\) None 0 12
1740.1.cn \(\chi_{1740}(43, \cdot)\) None 0 12
1740.1.cp \(\chi_{1740}(77, \cdot)\) None 0 12
1740.1.cq \(\chi_{1740}(293, \cdot)\) None 0 12
1740.1.cs \(\chi_{1740}(127, \cdot)\) None 0 12
1740.1.cu \(\chi_{1740}(13, \cdot)\) None 0 12
1740.1.cx \(\chi_{1740}(167, \cdot)\) None 0 12
1740.1.cz \(\chi_{1740}(229, \cdot)\) None 0 12
1740.1.da \(\chi_{1740}(11, \cdot)\) None 0 12

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1740))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1740)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(145))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(174))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(290))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(348))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(435))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(580))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(870))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1740))\)\(^{\oplus 1}\)