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Properties

Label 1836.1
Level 1836
Weight 1
Dimension 40
Nonzero newspaces 4
Newform subspaces 11
Sturm bound 186624
Trace bound 7

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Defining parameters

Level: \( N \) = \( 1836 = 2^{2} \cdot 3^{3} \cdot 17 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 11 \)
Sturm bound: \(186624\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1836))\).

Total New Old
Modular forms 2544 520 2024
Cusp forms 144 40 104
Eisenstein series 2400 480 1920

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 36 0 4 0

Trace form

\( 40 q - 4 q^{4} + 4 q^{7} + O(q^{10}) \) \( 40 q - 4 q^{4} + 4 q^{7} + 2 q^{13} - 4 q^{16} - 20 q^{17} + 2 q^{19} - 12 q^{21} + 2 q^{25} + 8 q^{26} + 2 q^{43} + 8 q^{53} + 2 q^{55} - 4 q^{61} - 4 q^{64} + 24 q^{66} + 4 q^{68} - 12 q^{69} - 4 q^{73} - 16 q^{77} + 4 q^{79} + 2 q^{85} + 4 q^{97} - 4 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1836))\)

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
1836.1.d \(\chi_{1836}(1565, \cdot)\) None 0 1
1836.1.e \(\chi_{1836}(271, \cdot)\) None 0 1
1836.1.f \(\chi_{1836}(919, \cdot)\) None 0 1
1836.1.g \(\chi_{1836}(917, \cdot)\) 1836.1.g.a 1 1
1836.1.g.b 1
1836.1.g.c 1
1836.1.g.d 1
1836.1.j \(\chi_{1836}(701, \cdot)\) 1836.1.j.a 4 2
1836.1.l \(\chi_{1836}(55, \cdot)\) None 0 2
1836.1.o \(\chi_{1836}(305, \cdot)\) None 0 2
1836.1.p \(\chi_{1836}(307, \cdot)\) None 0 2
1836.1.q \(\chi_{1836}(883, \cdot)\) 1836.1.q.a 2 2
1836.1.q.b 2
1836.1.q.c 4
1836.1.r \(\chi_{1836}(341, \cdot)\) None 0 2
1836.1.u \(\chi_{1836}(53, \cdot)\) None 0 4
1836.1.v \(\chi_{1836}(1243, \cdot)\) None 0 4
1836.1.z \(\chi_{1836}(89, \cdot)\) None 0 4
1836.1.bb \(\chi_{1836}(523, \cdot)\) None 0 4
1836.1.bf \(\chi_{1836}(109, \cdot)\) None 0 8
1836.1.bg \(\chi_{1836}(107, \cdot)\) None 0 8
1836.1.bi \(\chi_{1836}(137, \cdot)\) None 0 6
1836.1.bj \(\chi_{1836}(101, \cdot)\) None 0 6
1836.1.bm \(\chi_{1836}(103, \cdot)\) None 0 6
1836.1.bn \(\chi_{1836}(67, \cdot)\) 1836.1.bn.a 6 6
1836.1.bn.b 6
1836.1.bn.c 12
1836.1.bo \(\chi_{1836}(665, \cdot)\) None 0 8
1836.1.bp \(\chi_{1836}(19, \cdot)\) None 0 8
1836.1.bt \(\chi_{1836}(115, \cdot)\) None 0 12
1836.1.bv \(\chi_{1836}(149, \cdot)\) None 0 12
1836.1.by \(\chi_{1836}(71, \cdot)\) None 0 16
1836.1.bz \(\chi_{1836}(37, \cdot)\) None 0 16
1836.1.cc \(\chi_{1836}(77, \cdot)\) None 0 24
1836.1.cd \(\chi_{1836}(43, \cdot)\) None 0 24
1836.1.ce \(\chi_{1836}(61, \cdot)\) None 0 48
1836.1.cf \(\chi_{1836}(11, \cdot)\) None 0 48

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1836))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1836)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(102))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(153))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(204))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(306))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(459))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(612))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(918))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1836))\)\(^{\oplus 1}\)