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Properties

Label 3204.1
Level 3204
Weight 1
Dimension 189
Nonzero newspaces 10
Newform subspaces 20
Sturm bound 570240
Trace bound 7

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Defining parameters

Level: \( N \) = \( 3204 = 2^{2} \cdot 3^{2} \cdot 89 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 10 \)
Newform subspaces: \( 20 \)
Sturm bound: \(570240\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3204))\).

Total New Old
Modular forms 3796 971 2825
Cusp forms 276 189 87
Eisenstein series 3520 782 2738

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 181 0 8 0

Trace form

\( 189 q + q^{2} - 9 q^{4} + 6 q^{5} + 4 q^{7} + q^{8} + O(q^{10}) \) \( 189 q + q^{2} - 9 q^{4} + 6 q^{5} + 4 q^{7} + q^{8} - 2 q^{10} + 2 q^{13} - 9 q^{16} + 2 q^{17} + 6 q^{20} - 23 q^{25} + 2 q^{26} + 2 q^{29} + q^{32} - 6 q^{34} - 2 q^{37} - 2 q^{40} + 2 q^{41} - 13 q^{49} + 3 q^{50} - 2 q^{52} + 2 q^{53} - 2 q^{58} - 2 q^{61} + 27 q^{64} + 4 q^{65} + 2 q^{68} - 14 q^{73} - 20 q^{74} + 4 q^{79} - 16 q^{80} - 2 q^{82} + 4 q^{85} + 21 q^{89} - 12 q^{90} + 24 q^{93} + 6 q^{97} - 31 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3204))\)

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
3204.1.b \(\chi_{3204}(1601, \cdot)\) 3204.1.b.a 2 1
3204.1.b.b 2
3204.1.d \(\chi_{3204}(1781, \cdot)\) None 0 1
3204.1.f \(\chi_{3204}(1603, \cdot)\) None 0 1
3204.1.h \(\chi_{3204}(1423, \cdot)\) 3204.1.h.a 1 1
3204.1.h.b 1
3204.1.h.c 1
3204.1.h.d 2
3204.1.j \(\chi_{3204}(55, \cdot)\) 3204.1.j.a 2 2
3204.1.j.b 2
3204.1.l \(\chi_{3204}(233, \cdot)\) 3204.1.l.a 4 2
3204.1.n \(\chi_{3204}(355, \cdot)\) 3204.1.n.a 6 2
3204.1.n.b 6
3204.1.n.c 12
3204.1.p \(\chi_{3204}(535, \cdot)\) None 0 2
3204.1.r \(\chi_{3204}(713, \cdot)\) None 0 2
3204.1.t \(\chi_{3204}(533, \cdot)\) None 0 2
3204.1.u \(\chi_{3204}(215, \cdot)\) 3204.1.u.a 4 4
3204.1.u.b 4
3204.1.v \(\chi_{3204}(37, \cdot)\) None 0 4
3204.1.ba \(\chi_{3204}(1013, \cdot)\) None 0 4
3204.1.bc \(\chi_{3204}(835, \cdot)\) None 0 4
3204.1.bd \(\chi_{3204}(235, \cdot)\) 3204.1.bd.a 10 10
3204.1.bf \(\chi_{3204}(91, \cdot)\) 3204.1.bf.a 10 10
3204.1.bh \(\chi_{3204}(269, \cdot)\) None 0 10
3204.1.bj \(\chi_{3204}(413, \cdot)\) None 0 10
3204.1.bm \(\chi_{3204}(457, \cdot)\) None 0 8
3204.1.bn \(\chi_{3204}(635, \cdot)\) None 0 8
3204.1.bq \(\chi_{3204}(17, \cdot)\) None 0 20
3204.1.bs \(\chi_{3204}(199, \cdot)\) 3204.1.bs.a 20 20
3204.1.bs.b 20
3204.1.bt \(\chi_{3204}(317, \cdot)\) None 0 20
3204.1.bv \(\chi_{3204}(245, \cdot)\) None 0 20
3204.1.bx \(\chi_{3204}(67, \cdot)\) None 0 20
3204.1.bz \(\chi_{3204}(139, \cdot)\) None 0 20
3204.1.cc \(\chi_{3204}(145, \cdot)\) None 0 40
3204.1.cd \(\chi_{3204}(35, \cdot)\) 3204.1.cd.a 40 40
3204.1.cd.b 40
3204.1.ce \(\chi_{3204}(79, \cdot)\) None 0 40
3204.1.cg \(\chi_{3204}(5, \cdot)\) None 0 40
3204.1.ci \(\chi_{3204}(23, \cdot)\) None 0 80
3204.1.cj \(\chi_{3204}(13, \cdot)\) None 0 80

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3204))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3204)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(89))\)\(^{\oplus 9}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(178))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(267))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(356))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(534))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(801))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1068))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1602))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3204))\)\(^{\oplus 1}\)