Properties

Label 2520.1
Level 2520
Weight 1
Dimension 116
Nonzero newspaces 8
Newform subspaces 23
Sturm bound 331776
Trace bound 14

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Defining parameters

Level: \( N \) = \( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 23 \)
Sturm bound: \(331776\)
Trace bound: \(14\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2520))\).

Total New Old
Modular forms 5316 656 4660
Cusp forms 708 116 592
Eisenstein series 4608 540 4068

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 116 0 0 0

Trace form

\( 116q - 2q^{4} + 4q^{7} + O(q^{10}) \) \( 116q - 2q^{4} + 4q^{7} - 2q^{11} - 10q^{14} - 8q^{15} + 14q^{16} - 8q^{18} - 2q^{19} - 8q^{22} - 24q^{23} - 2q^{26} + 4q^{28} + 4q^{30} - 12q^{31} + 2q^{35} - 8q^{39} + 8q^{40} + 4q^{41} - 2q^{44} - 2q^{46} - 16q^{55} + 8q^{56} - 8q^{57} - 4q^{58} + 4q^{59} + 4q^{60} + 8q^{63} - 20q^{64} - 26q^{65} - 2q^{70} - 16q^{72} - 8q^{73} - 2q^{74} + 4q^{76} - 16q^{78} - 12q^{79} - 16q^{81} + 4q^{88} + 4q^{89} - 4q^{91} - 24q^{92} - 18q^{94} + 12q^{95} + 8q^{97} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2520))\)

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
2520.1.b \(\chi_{2520}(1259, \cdot)\) 2520.1.b.a 4 1
2520.1.b.b 4
2520.1.c \(\chi_{2520}(1639, \cdot)\) None 0 1
2520.1.h \(\chi_{2520}(1189, \cdot)\) 2520.1.h.a 1 1
2520.1.h.b 1
2520.1.h.c 1
2520.1.h.d 1
2520.1.h.e 4
2520.1.i \(\chi_{2520}(449, \cdot)\) None 0 1
2520.1.l \(\chi_{2520}(1961, \cdot)\) None 0 1
2520.1.m \(\chi_{2520}(181, \cdot)\) None 0 1
2520.1.n \(\chi_{2520}(631, \cdot)\) None 0 1
2520.1.o \(\chi_{2520}(251, \cdot)\) None 0 1
2520.1.r \(\chi_{2520}(701, \cdot)\) None 0 1
2520.1.s \(\chi_{2520}(1441, \cdot)\) None 0 1
2520.1.x \(\chi_{2520}(1891, \cdot)\) None 0 1
2520.1.y \(\chi_{2520}(1511, \cdot)\) None 0 1
2520.1.bb \(\chi_{2520}(2519, \cdot)\) None 0 1
2520.1.bc \(\chi_{2520}(379, \cdot)\) None 0 1
2520.1.bd \(\chi_{2520}(2449, \cdot)\) None 0 1
2520.1.be \(\chi_{2520}(1709, \cdot)\) None 0 1
2520.1.bk \(\chi_{2520}(323, \cdot)\) None 0 2
2520.1.bl \(\chi_{2520}(1063, \cdot)\) None 0 2
2520.1.bq \(\chi_{2520}(377, \cdot)\) None 0 2
2520.1.br \(\chi_{2520}(253, \cdot)\) None 0 2
2520.1.bs \(\chi_{2520}(1133, \cdot)\) None 0 2
2520.1.bt \(\chi_{2520}(1513, \cdot)\) None 0 2
2520.1.by \(\chi_{2520}(1583, \cdot)\) None 0 2
2520.1.bz \(\chi_{2520}(307, \cdot)\) None 0 2
2520.1.cc \(\chi_{2520}(1591, \cdot)\) None 0 2
2520.1.cd \(\chi_{2520}(1571, \cdot)\) None 0 2
2520.1.ce \(\chi_{2520}(1481, \cdot)\) None 0 2
2520.1.cf \(\chi_{2520}(61, \cdot)\) None 0 2
2520.1.ci \(\chi_{2520}(1069, \cdot)\) None 0 2
2520.1.cj \(\chi_{2520}(569, \cdot)\) None 0 2
2520.1.co \(\chi_{2520}(59, \cdot)\) None 0 2
2520.1.cp \(\chi_{2520}(79, \cdot)\) None 0 2
2520.1.cq \(\chi_{2520}(1151, \cdot)\) None 0 2
2520.1.cr \(\chi_{2520}(1171, \cdot)\) None 0 2
2520.1.cw \(\chi_{2520}(1081, \cdot)\) None 0 2
2520.1.cx \(\chi_{2520}(1061, \cdot)\) None 0 2
2520.1.da \(\chi_{2520}(1219, \cdot)\) None 0 2
2520.1.db \(\chi_{2520}(839, \cdot)\) None 0 2
2520.1.dd \(\chi_{2520}(149, \cdot)\) None 0 2
2520.1.de \(\chi_{2520}(1249, \cdot)\) None 0 2
2520.1.df \(\chi_{2520}(499, \cdot)\) None 0 2
2520.1.dg \(\chi_{2520}(479, \cdot)\) None 0 2
2520.1.dj \(\chi_{2520}(29, \cdot)\) None 0 2
2520.1.dk \(\chi_{2520}(769, \cdot)\) None 0 2
2520.1.dm \(\chi_{2520}(601, \cdot)\) None 0 2
2520.1.dn \(\chi_{2520}(1541, \cdot)\) None 0 2
2520.1.dq \(\chi_{2520}(1391, \cdot)\) None 0 2
2520.1.dr \(\chi_{2520}(1411, \cdot)\) None 0 2
2520.1.dw \(\chi_{2520}(241, \cdot)\) None 0 2
2520.1.dx \(\chi_{2520}(1661, \cdot)\) None 0 2
2520.1.ea \(\chi_{2520}(671, \cdot)\) None 0 2
2520.1.eb \(\chi_{2520}(211, \cdot)\) None 0 2
2520.1.ed \(\chi_{2520}(989, \cdot)\) None 0 2
2520.1.ee \(\chi_{2520}(649, \cdot)\) None 0 2
2520.1.ef \(\chi_{2520}(739, \cdot)\) 2520.1.ef.a 2 2
2520.1.ef.b 2
2520.1.ef.c 4
2520.1.ef.d 4
2520.1.eg \(\chi_{2520}(719, \cdot)\) None 0 2
2520.1.ej \(\chi_{2520}(809, \cdot)\) None 0 2
2520.1.ek \(\chi_{2520}(829, \cdot)\) 2520.1.ek.a 2 2
2520.1.ek.b 2
2520.1.ek.c 2
2520.1.ek.d 2
2520.1.ep \(\chi_{2520}(919, \cdot)\) None 0 2
2520.1.eq \(\chi_{2520}(899, \cdot)\) 2520.1.eq.a 8 2
2520.1.eq.b 8
2520.1.et \(\chi_{2520}(1021, \cdot)\) None 0 2
2520.1.eu \(\chi_{2520}(281, \cdot)\) None 0 2
2520.1.ex \(\chi_{2520}(131, \cdot)\) None 0 2
2520.1.ey \(\chi_{2520}(151, \cdot)\) None 0 2
2520.1.ez \(\chi_{2520}(1501, \cdot)\) None 0 2
2520.1.fa \(\chi_{2520}(401, \cdot)\) None 0 2
2520.1.fd \(\chi_{2520}(1091, \cdot)\) None 0 2
2520.1.fe \(\chi_{2520}(1471, \cdot)\) None 0 2
2520.1.fh \(\chi_{2520}(799, \cdot)\) None 0 2
2520.1.fi \(\chi_{2520}(419, \cdot)\) None 0 2
2520.1.fl \(\chi_{2520}(1409, \cdot)\) None 0 2
2520.1.fm \(\chi_{2520}(229, \cdot)\) None 0 2
2520.1.fr \(\chi_{2520}(1159, \cdot)\) None 0 2
2520.1.fs \(\chi_{2520}(1139, \cdot)\) None 0 2
2520.1.fv \(\chi_{2520}(1289, \cdot)\) None 0 2
2520.1.fw \(\chi_{2520}(349, \cdot)\) 2520.1.fw.a 8 2
2520.1.fw.b 8
2520.1.fz \(\chi_{2520}(971, \cdot)\) None 0 2
2520.1.ga \(\chi_{2520}(991, \cdot)\) None 0 2
2520.1.gb \(\chi_{2520}(901, \cdot)\) None 0 2
2520.1.gc \(\chi_{2520}(1241, \cdot)\) None 0 2
2520.1.gg \(\chi_{2520}(409, \cdot)\) None 0 2
2520.1.gh \(\chi_{2520}(1229, \cdot)\) None 0 2
2520.1.gi \(\chi_{2520}(1319, \cdot)\) None 0 2
2520.1.gj \(\chi_{2520}(1339, \cdot)\) None 0 2
2520.1.gm \(\chi_{2520}(331, \cdot)\) None 0 2
2520.1.gn \(\chi_{2520}(311, \cdot)\) None 0 2
2520.1.gs \(\chi_{2520}(221, \cdot)\) None 0 2
2520.1.gt \(\chi_{2520}(1321, \cdot)\) None 0 2
2520.1.gu \(\chi_{2520}(1213, \cdot)\) None 0 4
2520.1.gv \(\chi_{2520}(1193, \cdot)\) None 0 4
2520.1.ha \(\chi_{2520}(943, \cdot)\) None 0 4
2520.1.hb \(\chi_{2520}(347, \cdot)\) None 0 4
2520.1.he \(\chi_{2520}(337, \cdot)\) None 0 4
2520.1.hf \(\chi_{2520}(293, \cdot)\) 2520.1.hf.a 16 4
2520.1.hf.b 16
2520.1.hi \(\chi_{2520}(23, \cdot)\) None 0 4
2520.1.hj \(\chi_{2520}(1123, \cdot)\) None 0 4
2520.1.hm \(\chi_{2520}(523, \cdot)\) None 0 4
2520.1.hn \(\chi_{2520}(863, \cdot)\) None 0 4
2520.1.ho \(\chi_{2520}(793, \cdot)\) None 0 4
2520.1.hp \(\chi_{2520}(773, \cdot)\) None 0 4
2520.1.hs \(\chi_{2520}(1013, \cdot)\) None 0 4
2520.1.ht \(\chi_{2520}(1033, \cdot)\) None 0 4
2520.1.hw \(\chi_{2520}(643, \cdot)\) None 0 4
2520.1.hx \(\chi_{2520}(407, \cdot)\) None 0 4
2520.1.ic \(\chi_{2520}(223, \cdot)\) None 0 4
2520.1.id \(\chi_{2520}(1163, \cdot)\) None 0 4
2520.1.ig \(\chi_{2520}(257, \cdot)\) None 0 4
2520.1.ih \(\chi_{2520}(277, \cdot)\) None 0 4
2520.1.ik \(\chi_{2520}(37, \cdot)\) 2520.1.ik.a 8 4
2520.1.ik.b 8
2520.1.il \(\chi_{2520}(17, \cdot)\) None 0 4
2520.1.im \(\chi_{2520}(703, \cdot)\) None 0 4
2520.1.in \(\chi_{2520}(107, \cdot)\) None 0 4
2520.1.iq \(\chi_{2520}(1283, \cdot)\) None 0 4
2520.1.ir \(\chi_{2520}(103, \cdot)\) None 0 4
2520.1.iu \(\chi_{2520}(1093, \cdot)\) None 0 4
2520.1.iv \(\chi_{2520}(713, \cdot)\) None 0 4
2520.1.iy \(\chi_{2520}(187, \cdot)\) None 0 4
2520.1.iz \(\chi_{2520}(1103, \cdot)\) None 0 4
2520.1.je \(\chi_{2520}(193, \cdot)\) None 0 4
2520.1.jf \(\chi_{2520}(173, \cdot)\) None 0 4

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2520))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2520)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(280))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(315))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(360))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(420))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(504))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(840))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1260))\)\(^{\oplus 2}\)