↑

Properties

Label 2997.1
Level 2997
Weight 1
Dimension 98
Nonzero newspaces 14
Newform subspaces 21
Sturm bound 664848
Trace bound 103

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 2997 = 3^{4} \cdot 37 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 14 \)
Newform subspaces: \( 21 \)
Sturm bound: \(664848\)
Trace bound: \(103\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2997))\).

Total New Old
Modular forms 4108 2058 2050
Cusp forms 220 98 122
Eisenstein series 3888 1960 1928

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 90 0 8 0

Trace form

\( 98 q - 11 q^{4} + O(q^{10}) \) \( 98 q - 11 q^{4} - 24 q^{10} + 4 q^{13} - 7 q^{16} - 4 q^{19} - 4 q^{22} - 11 q^{25} - 24 q^{28} + 6 q^{31} + 4 q^{34} - 14 q^{37} + 8 q^{40} + 6 q^{43} - 16 q^{46} - 3 q^{49} + 8 q^{55} + 4 q^{58} - 2 q^{61} + 18 q^{64} + 12 q^{70} - 12 q^{73} + 2 q^{76} + 4 q^{79} + 4 q^{85} - 4 q^{91} - 2 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2997))\)

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
2997.1.b \(\chi_{2997}(2591, \cdot)\) None 0 1
2997.1.d \(\chi_{2997}(2996, \cdot)\) None 0 1
2997.1.i \(\chi_{2997}(487, \cdot)\) None 0 2
2997.1.l \(\chi_{2997}(26, \cdot)\) 2997.1.l.a 2 2
2997.1.l.b 4
2997.1.m \(\chi_{2997}(323, \cdot)\) None 0 2
2997.1.n \(\chi_{2997}(998, \cdot)\) 2997.1.n.a 2 2
2997.1.n.b 2
2997.1.n.c 2
2997.1.n.d 4
2997.1.n.e 4
2997.1.n.f 8
2997.1.o \(\chi_{2997}(1322, \cdot)\) 2997.1.o.a 2 2
2997.1.p \(\chi_{2997}(2024, \cdot)\) None 0 2
2997.1.r \(\chi_{2997}(593, \cdot)\) None 0 2
2997.1.u \(\chi_{2997}(269, \cdot)\) 2997.1.u.a 2 2
2997.1.u.b 4
2997.1.v \(\chi_{2997}(1565, \cdot)\) 2997.1.v.a 2 2
2997.1.bj \(\chi_{2997}(2080, \cdot)\) 2997.1.bj.a 4 4
2997.1.bk \(\chi_{2997}(82, \cdot)\) None 0 4
2997.1.bm \(\chi_{2997}(919, \cdot)\) 2997.1.bm.a 4 4
2997.1.bp \(\chi_{2997}(541, \cdot)\) 2997.1.bp.a 4 4
2997.1.bq \(\chi_{2997}(197, \cdot)\) None 0 6
2997.1.bs \(\chi_{2997}(953, \cdot)\) None 0 6
2997.1.bt \(\chi_{2997}(62, \cdot)\) None 0 6
2997.1.bu \(\chi_{2997}(521, \cdot)\) None 0 6
2997.1.bv \(\chi_{2997}(287, \cdot)\) None 0 6
2997.1.bx \(\chi_{2997}(440, \cdot)\) None 0 6
2997.1.bz \(\chi_{2997}(530, \cdot)\) None 0 6
2997.1.ca \(\chi_{2997}(215, \cdot)\) 2997.1.ca.a 6 6
2997.1.cb \(\chi_{2997}(899, \cdot)\) None 0 6
2997.1.cc \(\chi_{2997}(332, \cdot)\) None 0 6
2997.1.cd \(\chi_{2997}(233, \cdot)\) None 0 6
2997.1.ce \(\chi_{2997}(485, \cdot)\) None 0 6
2997.1.cf \(\chi_{2997}(188, \cdot)\) 2997.1.cf.a 6 6
2997.1.cg \(\chi_{2997}(377, \cdot)\) 2997.1.cg.a 6 6
2997.1.ck \(\chi_{2997}(602, \cdot)\) None 0 6
2997.1.cl \(\chi_{2997}(359, \cdot)\) None 0 6
2997.1.cm \(\chi_{2997}(260, \cdot)\) None 0 6
2997.1.cp \(\chi_{2997}(53, \cdot)\) 2997.1.cp.a 6 6
2997.1.cq \(\chi_{2997}(404, \cdot)\) None 0 6
2997.1.cs \(\chi_{2997}(206, \cdot)\) None 0 6
2997.1.ct \(\chi_{2997}(737, \cdot)\) None 0 6
2997.1.cw \(\chi_{2997}(773, \cdot)\) None 0 6
2997.1.cy \(\chi_{2997}(44, \cdot)\) None 0 6
2997.1.cz \(\chi_{2997}(152, \cdot)\) None 0 6
2997.1.dj \(\chi_{2997}(172, \cdot)\) None 0 12
2997.1.dl \(\chi_{2997}(91, \cdot)\) None 0 12
2997.1.dm \(\chi_{2997}(19, \cdot)\) None 0 12
2997.1.dp \(\chi_{2997}(190, \cdot)\) 2997.1.dp.a 12 12
2997.1.dv \(\chi_{2997}(154, \cdot)\) None 0 12
2997.1.dw \(\chi_{2997}(208, \cdot)\) None 0 12
2997.1.dx \(\chi_{2997}(199, \cdot)\) None 0 12
2997.1.dy \(\chi_{2997}(55, \cdot)\) 2997.1.dy.a 12 12
2997.1.dz \(\chi_{2997}(163, \cdot)\) None 0 12
2997.1.eb \(\chi_{2997}(505, \cdot)\) None 0 12
2997.1.ed \(\chi_{2997}(424, \cdot)\) None 0 12
2997.1.ee \(\chi_{2997}(388, \cdot)\) None 0 12
2997.1.eh \(\chi_{2997}(86, \cdot)\) None 0 18
2997.1.ej \(\chi_{2997}(95, \cdot)\) None 0 18
2997.1.ek \(\chi_{2997}(263, \cdot)\) None 0 18
2997.1.el \(\chi_{2997}(497, \cdot)\) None 0 18
2997.1.em \(\chi_{2997}(41, \cdot)\) None 0 18
2997.1.en \(\chi_{2997}(65, \cdot)\) None 0 18
2997.1.eo \(\chi_{2997}(83, \cdot)\) None 0 18
2997.1.ep \(\chi_{2997}(164, \cdot)\) None 0 18
2997.1.eq \(\chi_{2997}(374, \cdot)\) None 0 18
2997.1.eu \(\chi_{2997}(38, \cdot)\) None 0 18
2997.1.ev \(\chi_{2997}(137, \cdot)\) None 0 18
2997.1.ew \(\chi_{2997}(110, \cdot)\) None 0 18
2997.1.ex \(\chi_{2997}(11, \cdot)\) None 0 18
2997.1.ey \(\chi_{2997}(101, \cdot)\) None 0 18
2997.1.ez \(\chi_{2997}(47, \cdot)\) None 0 18
2997.1.fe \(\chi_{2997}(275, \cdot)\) None 0 18
2997.1.fg \(\chi_{2997}(182, \cdot)\) None 0 18
2997.1.fh \(\chi_{2997}(176, \cdot)\) None 0 18
2997.1.fl \(\chi_{2997}(88, \cdot)\) None 0 36
2997.1.fm \(\chi_{2997}(79, \cdot)\) None 0 36
2997.1.fn \(\chi_{2997}(22, \cdot)\) None 0 36
2997.1.fo \(\chi_{2997}(76, \cdot)\) None 0 36
2997.1.fp \(\chi_{2997}(214, \cdot)\) None 0 36
2997.1.fq \(\chi_{2997}(31, \cdot)\) None 0 36
2997.1.fx \(\chi_{2997}(187, \cdot)\) None 0 36
2997.1.fy \(\chi_{2997}(52, \cdot)\) None 0 36
2997.1.fz \(\chi_{2997}(13, \cdot)\) None 0 36

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2997))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2997)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(111))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(333))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(999))\)\(^{\oplus 2}\)