Properties

Label 2960.1
Level 2960
Weight 1
Dimension 80
Nonzero newspaces 13
Newform subspaces 17
Sturm bound 525312
Trace bound 17

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Defining parameters

Level: \( N \) = \( 2960 = 2^{4} \cdot 5 \cdot 37 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 13 \)
Newform subspaces: \( 17 \)
Sturm bound: \(525312\)
Trace bound: \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2960))\).

Total New Old
Modular forms 4546 1024 3522
Cusp forms 514 80 434
Eisenstein series 4032 944 3088

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 60 0 20 0

Trace form

\( 80q + 2q^{2} + 2q^{3} + 6q^{5} + 16q^{6} - 4q^{8} + 10q^{9} + O(q^{10}) \) \( 80q + 2q^{2} + 2q^{3} + 6q^{5} + 16q^{6} - 4q^{8} + 10q^{9} + 8q^{10} + 16q^{11} + 2q^{12} - 2q^{13} - 8q^{14} - 2q^{15} + 4q^{19} + 2q^{20} - 8q^{21} + 6q^{25} - 8q^{26} + 4q^{27} + 4q^{28} - 4q^{29} + 2q^{30} - 12q^{31} + 2q^{32} + 4q^{33} - 4q^{34} - 2q^{35} - 2q^{37} + 4q^{39} - 4q^{40} + 4q^{41} - 4q^{43} - 4q^{44} - 2q^{45} - 8q^{46} - 4q^{48} + 14q^{49} + 2q^{50} - 8q^{51} - 2q^{52} - 2q^{53} - 2q^{55} + 8q^{60} + 18q^{61} - 2q^{62} + 17q^{65} + 16q^{66} + 4q^{69} + 4q^{70} + 12q^{71} - 8q^{74} - 4q^{76} - 4q^{77} - 2q^{78} - 4q^{79} - 4q^{80} + 2q^{81} + 4q^{82} - 8q^{84} + q^{85} - 8q^{88} + 10q^{89} + 4q^{92} - 2q^{93} + 2q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2960))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
2960.1.b \(\chi_{2960}(591, \cdot)\) None 0 1
2960.1.c \(\chi_{2960}(2591, \cdot)\) None 0 1
2960.1.h \(\chi_{2960}(1479, \cdot)\) None 0 1
2960.1.i \(\chi_{2960}(519, \cdot)\) None 0 1
2960.1.l \(\chi_{2960}(1111, \cdot)\) None 0 1
2960.1.m \(\chi_{2960}(2071, \cdot)\) None 0 1
2960.1.n \(\chi_{2960}(1999, \cdot)\) None 0 1
2960.1.o \(\chi_{2960}(2959, \cdot)\) 2960.1.o.a 4 1
2960.1.o.b 4
2960.1.s \(\chi_{2960}(1289, \cdot)\) None 0 2
2960.1.u \(\chi_{2960}(2517, \cdot)\) None 0 2
2960.1.w \(\chi_{2960}(1227, \cdot)\) None 0 2
2960.1.x \(\chi_{2960}(1067, \cdot)\) None 0 2
2960.1.z \(\chi_{2960}(517, \cdot)\) None 0 2
2960.1.bb \(\chi_{2960}(401, \cdot)\) None 0 2
2960.1.be \(\chi_{2960}(1141, \cdot)\) None 0 2
2960.1.bf \(\chi_{2960}(1259, \cdot)\) None 0 2
2960.1.bi \(\chi_{2960}(739, \cdot)\) None 0 2
2960.1.bj \(\chi_{2960}(1301, \cdot)\) None 0 2
2960.1.bl \(\chi_{2960}(487, \cdot)\) None 0 2
2960.1.bn \(\chi_{2960}(73, \cdot)\) None 0 2
2960.1.bp \(\chi_{2960}(297, \cdot)\) None 0 2
2960.1.bs \(\chi_{2960}(327, \cdot)\) None 0 2
2960.1.bu \(\chi_{2960}(783, \cdot)\) 2960.1.bu.a 2 2
2960.1.bw \(\chi_{2960}(593, \cdot)\) None 0 2
2960.1.by \(\chi_{2960}(1553, \cdot)\) None 0 2
2960.1.bz \(\chi_{2960}(623, \cdot)\) 2960.1.bz.a 2 2
2960.1.cb \(\chi_{2960}(709, \cdot)\) None 0 2
2960.1.cd \(\chi_{2960}(1331, \cdot)\) None 0 2
2960.1.cg \(\chi_{2960}(371, \cdot)\) None 0 2
2960.1.ci \(\chi_{2960}(549, \cdot)\) None 0 2
2960.1.cj \(\chi_{2960}(2769, \cdot)\) 2960.1.cj.a 2 2
2960.1.cj.b 2
2960.1.cm \(\chi_{2960}(1997, \cdot)\) None 0 2
2960.1.co \(\chi_{2960}(2707, \cdot)\) None 0 2
2960.1.cp \(\chi_{2960}(43, \cdot)\) None 0 2
2960.1.cr \(\chi_{2960}(1037, \cdot)\) None 0 2
2960.1.cu \(\chi_{2960}(1881, \cdot)\) None 0 2
2960.1.cv \(\chi_{2960}(159, \cdot)\) None 0 2
2960.1.cw \(\chi_{2960}(639, \cdot)\) 2960.1.cw.a 2 2
2960.1.cw.b 2
2960.1.da \(\chi_{2960}(471, \cdot)\) None 0 2
2960.1.db \(\chi_{2960}(951, \cdot)\) None 0 2
2960.1.de \(\chi_{2960}(359, \cdot)\) None 0 2
2960.1.df \(\chi_{2960}(1639, \cdot)\) None 0 2
2960.1.dg \(\chi_{2960}(1231, \cdot)\) None 0 2
2960.1.dh \(\chi_{2960}(751, \cdot)\) None 0 2
2960.1.dm \(\chi_{2960}(1081, \cdot)\) None 0 4
2960.1.dn \(\chi_{2960}(877, \cdot)\) 2960.1.dn.a 4 4
2960.1.dp \(\chi_{2960}(547, \cdot)\) None 0 4
2960.1.ds \(\chi_{2960}(467, \cdot)\) None 0 4
2960.1.du \(\chi_{2960}(397, \cdot)\) None 0 4
2960.1.dv \(\chi_{2960}(689, \cdot)\) None 0 4
2960.1.dy \(\chi_{2960}(1229, \cdot)\) None 0 4
2960.1.ea \(\chi_{2960}(211, \cdot)\) None 0 4
2960.1.eb \(\chi_{2960}(11, \cdot)\) None 0 4
2960.1.ed \(\chi_{2960}(29, \cdot)\) None 0 4
2960.1.ef \(\chi_{2960}(23, \cdot)\) None 0 4
2960.1.ei \(\chi_{2960}(137, \cdot)\) None 0 4
2960.1.ek \(\chi_{2960}(233, \cdot)\) None 0 4
2960.1.em \(\chi_{2960}(103, \cdot)\) None 0 4
2960.1.eo \(\chi_{2960}(1007, \cdot)\) 2960.1.eo.a 4 4
2960.1.ep \(\chi_{2960}(1137, \cdot)\) None 0 4
2960.1.er \(\chi_{2960}(417, \cdot)\) None 0 4
2960.1.et \(\chi_{2960}(1087, \cdot)\) 2960.1.et.a 4 4
2960.1.ev \(\chi_{2960}(341, \cdot)\) None 0 4
2960.1.ey \(\chi_{2960}(619, \cdot)\) None 0 4
2960.1.ez \(\chi_{2960}(1099, \cdot)\) 2960.1.ez.a 8 4
2960.1.fc \(\chi_{2960}(421, \cdot)\) None 0 4
2960.1.fd \(\chi_{2960}(1281, \cdot)\) None 0 4
2960.1.ff \(\chi_{2960}(677, \cdot)\) None 0 4
2960.1.fh \(\chi_{2960}(347, \cdot)\) None 0 4
2960.1.fk \(\chi_{2960}(267, \cdot)\) None 0 4
2960.1.fm \(\chi_{2960}(1157, \cdot)\) 2960.1.fm.a 4 4
2960.1.fo \(\chi_{2960}(489, \cdot)\) None 0 4
2960.1.fp \(\chi_{2960}(151, \cdot)\) None 0 6
2960.1.fq \(\chi_{2960}(599, \cdot)\) None 0 6
2960.1.ft \(\chi_{2960}(71, \cdot)\) None 0 6
2960.1.fv \(\chi_{2960}(839, \cdot)\) None 0 6
2960.1.fx \(\chi_{2960}(719, \cdot)\) 2960.1.fx.a 6 6
2960.1.fx.b 6
2960.1.fz \(\chi_{2960}(511, \cdot)\) None 0 6
2960.1.ga \(\chi_{2960}(559, \cdot)\) None 0 6
2960.1.gc \(\chi_{2960}(271, \cdot)\) None 0 6
2960.1.gf \(\chi_{2960}(383, \cdot)\) 2960.1.gf.a 12 12
2960.1.gg \(\chi_{2960}(281, \cdot)\) None 0 12
2960.1.gj \(\chi_{2960}(337, \cdot)\) None 0 12
2960.1.gk \(\chi_{2960}(33, \cdot)\) None 0 12
2960.1.gn \(\chi_{2960}(89, \cdot)\) None 0 12
2960.1.go \(\chi_{2960}(143, \cdot)\) 2960.1.go.a 12 12
2960.1.gr \(\chi_{2960}(203, \cdot)\) None 0 12
2960.1.gt \(\chi_{2960}(451, \cdot)\) None 0 12
2960.1.gu \(\chi_{2960}(99, \cdot)\) None 0 12
2960.1.gw \(\chi_{2960}(163, \cdot)\) None 0 12
2960.1.gz \(\chi_{2960}(77, \cdot)\) None 0 12
2960.1.ha \(\chi_{2960}(53, \cdot)\) None 0 12
2960.1.hc \(\chi_{2960}(69, \cdot)\) None 0 12
2960.1.he \(\chi_{2960}(261, \cdot)\) None 0 12
2960.1.hh \(\chi_{2960}(61, \cdot)\) None 0 12
2960.1.hj \(\chi_{2960}(309, \cdot)\) None 0 12
2960.1.hk \(\chi_{2960}(173, \cdot)\) None 0 12
2960.1.hn \(\chi_{2960}(197, \cdot)\) None 0 12
2960.1.ho \(\chi_{2960}(523, \cdot)\) None 0 12
2960.1.hq \(\chi_{2960}(219, \cdot)\) None 0 12
2960.1.ht \(\chi_{2960}(411, \cdot)\) None 0 12
2960.1.hv \(\chi_{2960}(187, \cdot)\) None 0 12
2960.1.hw \(\chi_{2960}(183, \cdot)\) None 0 12
2960.1.hz \(\chi_{2960}(129, \cdot)\) None 0 12
2960.1.ib \(\chi_{2960}(377, \cdot)\) None 0 12
2960.1.ic \(\chi_{2960}(617, \cdot)\) None 0 12
2960.1.ie \(\chi_{2960}(161, \cdot)\) None 0 12
2960.1.ih \(\chi_{2960}(87, \cdot)\) None 0 12

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2960))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2960)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(148))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(296))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(592))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(740))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1480))\)\(^{\oplus 2}\)