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Properties

Label 3025.1
Level 3025
Weight 1
Dimension 106
Nonzero newspaces 16
Newform subspaces 20
Sturm bound 726000
Trace bound 25

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Defining parameters

Level: \( N \) = \( 3025 = 5^{2} \cdot 11^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 16 \)
Newform subspaces: \( 20 \)
Sturm bound: \(726000\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3025))\).

Total New Old
Modular forms 4636 2986 1650
Cusp forms 156 106 50
Eisenstein series 4480 2880 1600

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 106 0 0 0

Trace form

\( 106 q + 2 q^{3} - q^{4} + 5 q^{9} + O(q^{10}) \) \( 106 q + 2 q^{3} - q^{4} + 5 q^{9} + 12 q^{12} + 2 q^{15} + q^{16} + 2 q^{20} + 12 q^{23} - 8 q^{25} - 6 q^{27} + 2 q^{31} + 3 q^{36} + 2 q^{37} - 18 q^{45} + 2 q^{47} + 2 q^{48} - q^{49} + 2 q^{53} - 4 q^{59} - 8 q^{60} - q^{64} - 28 q^{67} + 4 q^{69} + 2 q^{71} + 2 q^{75} + 5 q^{81} + 8 q^{89} - 8 q^{92} - 6 q^{93} + 2 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3025))\)

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
3025.1.c \(\chi_{3025}(1451, \cdot)\) None 0 1
3025.1.d \(\chi_{3025}(3024, \cdot)\) None 0 1
3025.1.f \(\chi_{3025}(243, \cdot)\) 3025.1.f.a 2 2
3025.1.f.b 2
3025.1.f.c 2
3025.1.m \(\chi_{3025}(161, \cdot)\) 3025.1.m.a 4 4
3025.1.o \(\chi_{3025}(94, \cdot)\) 3025.1.o.a 4 4
3025.1.p \(\chi_{3025}(959, \cdot)\) 3025.1.p.a 4 4
3025.1.q \(\chi_{3025}(524, \cdot)\) None 0 4
3025.1.r \(\chi_{3025}(844, \cdot)\) 3025.1.r.a 4 4
3025.1.s \(\chi_{3025}(604, \cdot)\) None 0 4
3025.1.u \(\chi_{3025}(336, \cdot)\) 3025.1.u.a 4 4
3025.1.v \(\chi_{3025}(241, \cdot)\) None 0 4
3025.1.w \(\chi_{3025}(481, \cdot)\) 3025.1.w.a 4 4
3025.1.x \(\chi_{3025}(1201, \cdot)\) 3025.1.x.a 4 4
3025.1.bc \(\chi_{3025}(596, \cdot)\) 3025.1.bc.a 4 4
3025.1.bd \(\chi_{3025}(1304, \cdot)\) 3025.1.bd.a 4 4
3025.1.bf \(\chi_{3025}(202, \cdot)\) 3025.1.bf.a 8 8
3025.1.bi \(\chi_{3025}(372, \cdot)\) 3025.1.bi.a 8 8
3025.1.bj \(\chi_{3025}(122, \cdot)\) 3025.1.bj.a 8 8
3025.1.bk \(\chi_{3025}(608, \cdot)\) 3025.1.bk.a 8 8
3025.1.bl \(\chi_{3025}(493, \cdot)\) 3025.1.bl.a 8 8
3025.1.bl.b 8
3025.1.bl.c 8
3025.1.bq \(\chi_{3025}(3, \cdot)\) 3025.1.bq.a 8 8
3025.1.br \(\chi_{3025}(274, \cdot)\) None 0 10
3025.1.bt \(\chi_{3025}(76, \cdot)\) None 0 10
3025.1.bu \(\chi_{3025}(232, \cdot)\) None 0 20
3025.1.cc \(\chi_{3025}(139, \cdot)\) None 0 40
3025.1.ce \(\chi_{3025}(51, \cdot)\) None 0 40
3025.1.cf \(\chi_{3025}(116, \cdot)\) None 0 40
3025.1.cg \(\chi_{3025}(21, \cdot)\) None 0 40
3025.1.ch \(\chi_{3025}(61, \cdot)\) None 0 40
3025.1.cm \(\chi_{3025}(6, \cdot)\) None 0 40
3025.1.cn \(\chi_{3025}(79, \cdot)\) None 0 40
3025.1.co \(\chi_{3025}(54, \cdot)\) None 0 40
3025.1.cp \(\chi_{3025}(19, \cdot)\) None 0 40
3025.1.cq \(\chi_{3025}(24, \cdot)\) None 0 40
3025.1.cr \(\chi_{3025}(39, \cdot)\) None 0 40
3025.1.cs \(\chi_{3025}(41, \cdot)\) None 0 40
3025.1.cu \(\chi_{3025}(47, \cdot)\) None 0 80
3025.1.cz \(\chi_{3025}(37, \cdot)\) None 0 80
3025.1.da \(\chi_{3025}(82, \cdot)\) None 0 80
3025.1.db \(\chi_{3025}(38, \cdot)\) None 0 80
3025.1.dc \(\chi_{3025}(12, \cdot)\) None 0 80
3025.1.df \(\chi_{3025}(42, \cdot)\) None 0 80

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3025))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3025)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(275))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(605))\)\(^{\oplus 2}\)