Properties

Label 3675.1
Level 3675
Weight 1
Dimension 292
Nonzero newspaces 12
Newform subspaces 35
Sturm bound 940800
Trace bound 16

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Defining parameters

Level: \( N \) = \( 3675 = 3 \cdot 5^{2} \cdot 7^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 35 \)
Sturm bound: \(940800\)
Trace bound: \(16\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3675))\).

Total New Old
Modular forms 7174 2281 4893
Cusp forms 454 292 162
Eisenstein series 6720 1989 4731

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 244 0 48 0

Trace form

\( 292 q + q^{3} + q^{4} + q^{7} + q^{9} + O(q^{10}) \) \( 292 q + q^{3} + q^{4} + q^{7} + q^{9} + q^{12} + 2 q^{13} + 5 q^{16} + 2 q^{19} + q^{21} + q^{27} + q^{28} + 10 q^{31} - 49 q^{36} - 5 q^{37} - 5 q^{39} + 2 q^{43} - 6 q^{48} + q^{49} - 5 q^{52} + 2 q^{57} + 3 q^{61} - 6 q^{63} + 19 q^{64} + 2 q^{67} + 2 q^{73} + 10 q^{76} + 2 q^{79} + 5 q^{81} + q^{84} + 2 q^{91} + 2 q^{93} + 2 q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3675))\)

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
3675.1.c \(\chi_{3675}(1226, \cdot)\) 3675.1.c.a 1 1
3675.1.c.b 1
3675.1.c.c 1
3675.1.c.d 1
3675.1.c.e 2
3675.1.c.f 4
3675.1.c.g 4
3675.1.c.h 4
3675.1.e \(\chi_{3675}(2449, \cdot)\) None 0 1
3675.1.f \(\chi_{3675}(2549, \cdot)\) 3675.1.f.a 2 1
3675.1.f.b 2
3675.1.f.c 4
3675.1.f.d 4
3675.1.h \(\chi_{3675}(1126, \cdot)\) None 0 1
3675.1.k \(\chi_{3675}(293, \cdot)\) 3675.1.k.a 8 2
3675.1.k.b 8
3675.1.k.c 8
3675.1.l \(\chi_{3675}(1618, \cdot)\) None 0 2
3675.1.o \(\chi_{3675}(901, \cdot)\) None 0 2
3675.1.p \(\chi_{3675}(2174, \cdot)\) 3675.1.p.a 4 2
3675.1.p.b 8
3675.1.p.c 8
3675.1.s \(\chi_{3675}(2224, \cdot)\) None 0 2
3675.1.u \(\chi_{3675}(851, \cdot)\) 3675.1.u.a 2 2
3675.1.u.b 2
3675.1.u.c 4
3675.1.u.d 8
3675.1.u.e 8
3675.1.u.f 8
3675.1.w \(\chi_{3675}(391, \cdot)\) None 0 4
3675.1.y \(\chi_{3675}(344, \cdot)\) None 0 4
3675.1.z \(\chi_{3675}(244, \cdot)\) None 0 4
3675.1.bb \(\chi_{3675}(491, \cdot)\) None 0 4
3675.1.be \(\chi_{3675}(1243, \cdot)\) None 0 4
3675.1.bf \(\chi_{3675}(68, \cdot)\) 3675.1.bf.a 8 4
3675.1.bf.b 8
3675.1.bf.c 16
3675.1.bf.d 16
3675.1.bh \(\chi_{3675}(76, \cdot)\) None 0 6
3675.1.bj \(\chi_{3675}(449, \cdot)\) 3675.1.bj.a 12 6
3675.1.bk \(\chi_{3675}(349, \cdot)\) None 0 6
3675.1.bm \(\chi_{3675}(176, \cdot)\) 3675.1.bm.a 6 6
3675.1.bq \(\chi_{3675}(148, \cdot)\) None 0 8
3675.1.br \(\chi_{3675}(587, \cdot)\) None 0 8
3675.1.bu \(\chi_{3675}(43, \cdot)\) None 0 12
3675.1.bx \(\chi_{3675}(482, \cdot)\) 3675.1.bx.a 24 12
3675.1.by \(\chi_{3675}(116, \cdot)\) None 0 8
3675.1.ca \(\chi_{3675}(19, \cdot)\) None 0 8
3675.1.cd \(\chi_{3675}(569, \cdot)\) None 0 8
3675.1.ce \(\chi_{3675}(31, \cdot)\) None 0 8
3675.1.cg \(\chi_{3675}(326, \cdot)\) 3675.1.cg.a 12 12
3675.1.cg.b 12
3675.1.ci \(\chi_{3675}(124, \cdot)\) None 0 12
3675.1.cl \(\chi_{3675}(74, \cdot)\) 3675.1.cl.a 24 12
3675.1.cm \(\chi_{3675}(376, \cdot)\) None 0 12
3675.1.co \(\chi_{3675}(227, \cdot)\) None 0 16
3675.1.cp \(\chi_{3675}(67, \cdot)\) None 0 16
3675.1.cs \(\chi_{3675}(71, \cdot)\) None 0 24
3675.1.cu \(\chi_{3675}(34, \cdot)\) None 0 24
3675.1.cv \(\chi_{3675}(29, \cdot)\) None 0 24
3675.1.cx \(\chi_{3675}(181, \cdot)\) None 0 24
3675.1.cy \(\chi_{3675}(143, \cdot)\) 3675.1.cy.a 48 24
3675.1.db \(\chi_{3675}(193, \cdot)\) None 0 24
3675.1.dd \(\chi_{3675}(62, \cdot)\) None 0 48
3675.1.dg \(\chi_{3675}(22, \cdot)\) None 0 48
3675.1.dh \(\chi_{3675}(61, \cdot)\) None 0 48
3675.1.di \(\chi_{3675}(44, \cdot)\) None 0 48
3675.1.dl \(\chi_{3675}(94, \cdot)\) None 0 48
3675.1.dn \(\chi_{3675}(11, \cdot)\) None 0 48
3675.1.do \(\chi_{3675}(37, \cdot)\) None 0 96
3675.1.dr \(\chi_{3675}(17, \cdot)\) None 0 96

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3675))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3675)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(525))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(735))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1225))\)\(^{\oplus 2}\)