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Properties

Label 3636.1
Level 3636
Weight 1
Dimension 238
Nonzero newspaces 11
Newform subspaces 19
Sturm bound 734400
Trace bound 4

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Defining parameters

Level: \( N \) = \( 3636 = 2^{2} \cdot 3^{2} \cdot 101 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 11 \)
Newform subspaces: \( 19 \)
Sturm bound: \(734400\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3636))\).

Total New Old
Modular forms 4366 1128 3238
Cusp forms 366 238 128
Eisenstein series 4000 890 3110

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 216 0 6 16

Trace form

\( 238 q + 3 q^{2} - 5 q^{4} + 2 q^{7} - 3 q^{8} - 2 q^{9} + O(q^{10}) \) \( 238 q + 3 q^{2} - 5 q^{4} + 2 q^{7} - 3 q^{8} - 2 q^{9} - 18 q^{10} + 2 q^{11} + 2 q^{14} - 9 q^{16} + 12 q^{17} + 4 q^{18} + 6 q^{19} + 2 q^{20} - 6 q^{21} - 2 q^{22} - 21 q^{25} + 2 q^{26} + 2 q^{29} - 6 q^{31} - 7 q^{32} + 6 q^{33} + 4 q^{34} - 2 q^{35} + 8 q^{36} - 8 q^{37} - 4 q^{40} - 6 q^{41} - 8 q^{42} + 2 q^{45} - 25 q^{49} + 3 q^{50} - 8 q^{52} + 4 q^{53} + 2 q^{55} + 2 q^{56} + 4 q^{57} - 6 q^{58} + 2 q^{59} + 31 q^{64} + 8 q^{65} - 12 q^{66} - 2 q^{67} - 16 q^{69} - 4 q^{70} - 2 q^{71} - 2 q^{72} - 2 q^{73} + 2 q^{74} - 10 q^{76} + 12 q^{77} + 6 q^{79} + 8 q^{80} + 2 q^{81} - 37 q^{82} + 4 q^{84} - 14 q^{85} + 8 q^{88} + 12 q^{89} + 2 q^{90} + 2 q^{91} - 2 q^{95} - 4 q^{97} - 7 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3636))\)

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
3636.1.c \(\chi_{3636}(1817, \cdot)\) None 0 1
3636.1.e \(\chi_{3636}(809, \cdot)\) None 0 1
3636.1.f \(\chi_{3636}(1819, \cdot)\) None 0 1
3636.1.h \(\chi_{3636}(2827, \cdot)\) 3636.1.h.a 2 1
3636.1.h.b 3
3636.1.h.c 3
3636.1.h.d 8
3636.1.j \(\chi_{3636}(899, \cdot)\) 3636.1.j.a 4 2
3636.1.m \(\chi_{3636}(1909, \cdot)\) 3636.1.m.a 2 2
3636.1.m.b 2
3636.1.m.c 2
3636.1.o \(\chi_{3636}(403, \cdot)\) 3636.1.o.a 2 2
3636.1.o.b 2
3636.1.o.c 12
3636.1.o.d 12
3636.1.p \(\chi_{3636}(607, \cdot)\) None 0 2
3636.1.s \(\chi_{3636}(2021, \cdot)\) None 0 2
3636.1.u \(\chi_{3636}(605, \cdot)\) None 0 2
3636.1.v \(\chi_{3636}(1027, \cdot)\) 3636.1.v.a 8 4
3636.1.x \(\chi_{3636}(1711, \cdot)\) 3636.1.x.a 4 4
3636.1.y \(\chi_{3636}(701, \cdot)\) None 0 4
3636.1.ba \(\chi_{3636}(17, \cdot)\) None 0 4
3636.1.bd \(\chi_{3636}(313, \cdot)\) None 0 4
3636.1.be \(\chi_{3636}(515, \cdot)\) None 0 4
3636.1.bh \(\chi_{3636}(145, \cdot)\) None 0 8
3636.1.bk \(\chi_{3636}(647, \cdot)\) 3636.1.bk.a 16 8
3636.1.bm \(\chi_{3636}(65, \cdot)\) None 0 8
3636.1.bo \(\chi_{3636}(137, \cdot)\) None 0 8
3636.1.br \(\chi_{3636}(499, \cdot)\) 3636.1.br.a 16 8
3636.1.bs \(\chi_{3636}(115, \cdot)\) None 0 8
3636.1.bt \(\chi_{3636}(19, \cdot)\) 3636.1.bt.a 20 20
3636.1.bv \(\chi_{3636}(235, \cdot)\) 3636.1.bv.a 40 20
3636.1.bw \(\chi_{3636}(197, \cdot)\) None 0 20
3636.1.bz \(\chi_{3636}(125, \cdot)\) None 0 20
3636.1.cb \(\chi_{3636}(335, \cdot)\) None 0 16
3636.1.cc \(\chi_{3636}(133, \cdot)\) None 0 16
3636.1.cf \(\chi_{3636}(35, \cdot)\) 3636.1.cf.a 80 40
3636.1.ch \(\chi_{3636}(73, \cdot)\) None 0 40
3636.1.ck \(\chi_{3636}(43, \cdot)\) None 0 40
3636.1.cl \(\chi_{3636}(31, \cdot)\) None 0 40
3636.1.cn \(\chi_{3636}(5, \cdot)\) None 0 40
3636.1.co \(\chi_{3636}(77, \cdot)\) None 0 40
3636.1.cr \(\chi_{3636}(11, \cdot)\) None 0 80
3636.1.ct \(\chi_{3636}(61, \cdot)\) None 0 80

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3636))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3636)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(101))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(202))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(303))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(404))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(606))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(909))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1212))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1818))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3636))\)\(^{\oplus 1}\)