Properties

Label 2280.2
Level 2280
Weight 2
Dimension 52756
Nonzero newspaces 54
Sturm bound 552960
Trace bound 15

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Defining parameters

Level: \( N \) = \( 2280 = 2^{3} \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 54 \)
Sturm bound: \(552960\)
Trace bound: \(15\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2280))\).

Total New Old
Modular forms 141696 53572 88124
Cusp forms 134785 52756 82029
Eisenstein series 6911 816 6095

Trace form

\( 52756q - 8q^{2} - 40q^{3} - 72q^{4} - 8q^{5} - 84q^{6} - 88q^{7} + 16q^{8} - 72q^{9} + O(q^{10}) \) \( 52756q - 8q^{2} - 40q^{3} - 72q^{4} - 8q^{5} - 84q^{6} - 88q^{7} + 16q^{8} - 72q^{9} - 84q^{10} + 28q^{12} - 16q^{13} + 64q^{14} - 18q^{15} - 120q^{16} + 4q^{18} - 32q^{19} + 64q^{20} + 32q^{21} - 8q^{22} + 48q^{23} - 20q^{24} - 200q^{25} + 32q^{26} + 38q^{27} - 72q^{28} - 24q^{29} - 46q^{30} - 144q^{31} - 48q^{32} - 100q^{33} - 104q^{34} + 24q^{35} - 92q^{36} + 8q^{37} - 40q^{38} - 140q^{39} - 236q^{40} - 72q^{41} - 100q^{42} - 168q^{43} - 112q^{44} - 78q^{45} - 344q^{46} - 104q^{47} - 180q^{48} - 168q^{49} - 104q^{50} - 246q^{51} - 56q^{52} - 32q^{53} - 108q^{54} - 76q^{55} - 32q^{56} - 72q^{57} - 176q^{58} - 48q^{59} - 162q^{60} - 24q^{61} + 344q^{62} - 128q^{63} + 408q^{64} + 140q^{65} + 52q^{66} + 312q^{67} + 392q^{68} + 180q^{70} + 184q^{71} + 36q^{72} + 340q^{73} + 464q^{74} - 84q^{75} + 472q^{76} + 216q^{77} + 180q^{78} + 304q^{79} + 128q^{80} - 120q^{81} + 752q^{82} + 56q^{83} + 252q^{84} + 128q^{85} + 536q^{86} + 60q^{87} + 600q^{88} + 296q^{89} - 90q^{90} + 200q^{91} + 376q^{92} + 100q^{93} + 328q^{94} - 24q^{95} + 8q^{96} - 96q^{97} + 200q^{98} - 86q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2280))\)

We only show spaces with even 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
2280.2.a \(\chi_{2280}(1, \cdot)\) 2280.2.a.a 1 1
2280.2.a.b 1
2280.2.a.c 1
2280.2.a.d 1
2280.2.a.e 1
2280.2.a.f 1
2280.2.a.g 1
2280.2.a.h 1
2280.2.a.i 1
2280.2.a.j 1
2280.2.a.k 2
2280.2.a.l 2
2280.2.a.m 2
2280.2.a.n 2
2280.2.a.o 2
2280.2.a.p 2
2280.2.a.q 2
2280.2.a.r 3
2280.2.a.s 3
2280.2.a.t 3
2280.2.a.u 3
2280.2.c \(\chi_{2280}(1331, \cdot)\) n/a 288 1
2280.2.d \(\chi_{2280}(151, \cdot)\) None 0 1
2280.2.f \(\chi_{2280}(229, \cdot)\) n/a 216 1
2280.2.i \(\chi_{2280}(569, \cdot)\) n/a 120 1
2280.2.j \(\chi_{2280}(1369, \cdot)\) 2280.2.j.a 2 1
2280.2.j.b 2
2280.2.j.c 2
2280.2.j.d 2
2280.2.j.e 2
2280.2.j.f 6
2280.2.j.g 10
2280.2.j.h 12
2280.2.j.i 18
2280.2.m \(\chi_{2280}(1709, \cdot)\) n/a 472 1
2280.2.o \(\chi_{2280}(191, \cdot)\) None 0 1
2280.2.p \(\chi_{2280}(1291, \cdot)\) n/a 160 1
2280.2.r \(\chi_{2280}(1481, \cdot)\) 2280.2.r.a 40 1
2280.2.r.b 40
2280.2.u \(\chi_{2280}(1141, \cdot)\) n/a 144 1
2280.2.w \(\chi_{2280}(1519, \cdot)\) None 0 1
2280.2.x \(\chi_{2280}(419, \cdot)\) n/a 432 1
2280.2.ba \(\chi_{2280}(379, \cdot)\) n/a 240 1
2280.2.bb \(\chi_{2280}(1559, \cdot)\) None 0 1
2280.2.bd \(\chi_{2280}(341, \cdot)\) n/a 320 1
2280.2.bg \(\chi_{2280}(121, \cdot)\) 2280.2.bg.a 2 2
2280.2.bg.b 2
2280.2.bg.c 2
2280.2.bg.d 2
2280.2.bg.e 2
2280.2.bg.f 2
2280.2.bg.g 2
2280.2.bg.h 2
2280.2.bg.i 2
2280.2.bg.j 2
2280.2.bg.k 2
2280.2.bg.l 4
2280.2.bg.m 4
2280.2.bg.n 4
2280.2.bg.o 4
2280.2.bg.p 4
2280.2.bg.q 4
2280.2.bg.r 4
2280.2.bg.s 6
2280.2.bg.t 8
2280.2.bg.u 8
2280.2.bg.v 8
2280.2.bh \(\chi_{2280}(37, \cdot)\) n/a 480 2
2280.2.bk \(\chi_{2280}(343, \cdot)\) None 0 2
2280.2.bm \(\chi_{2280}(1217, \cdot)\) n/a 216 2
2280.2.bn \(\chi_{2280}(227, \cdot)\) n/a 944 2
2280.2.bp \(\chi_{2280}(77, \cdot)\) n/a 864 2
2280.2.bs \(\chi_{2280}(1367, \cdot)\) None 0 2
2280.2.bu \(\chi_{2280}(1177, \cdot)\) n/a 120 2
2280.2.bv \(\chi_{2280}(1027, \cdot)\) n/a 432 2
2280.2.bx \(\chi_{2280}(449, \cdot)\) n/a 240 2
2280.2.ca \(\chi_{2280}(349, \cdot)\) n/a 480 2
2280.2.cc \(\chi_{2280}(31, \cdot)\) None 0 2
2280.2.cd \(\chi_{2280}(11, \cdot)\) n/a 640 2
2280.2.cg \(\chi_{2280}(331, \cdot)\) n/a 320 2
2280.2.ch \(\chi_{2280}(311, \cdot)\) None 0 2
2280.2.cj \(\chi_{2280}(749, \cdot)\) n/a 944 2
2280.2.cm \(\chi_{2280}(49, \cdot)\) n/a 120 2
2280.2.co \(\chi_{2280}(539, \cdot)\) n/a 944 2
2280.2.cp \(\chi_{2280}(559, \cdot)\) None 0 2
2280.2.cr \(\chi_{2280}(1261, \cdot)\) n/a 320 2
2280.2.cu \(\chi_{2280}(521, \cdot)\) n/a 160 2
2280.2.cx \(\chi_{2280}(221, \cdot)\) n/a 640 2
2280.2.cz \(\chi_{2280}(239, \cdot)\) None 0 2
2280.2.da \(\chi_{2280}(259, \cdot)\) n/a 480 2
2280.2.dc \(\chi_{2280}(481, \cdot)\) n/a 240 6
2280.2.de \(\chi_{2280}(107, \cdot)\) n/a 1888 4
2280.2.df \(\chi_{2280}(353, \cdot)\) n/a 480 4
2280.2.dh \(\chi_{2280}(7, \cdot)\) None 0 4
2280.2.dk \(\chi_{2280}(373, \cdot)\) n/a 960 4
2280.2.dm \(\chi_{2280}(163, \cdot)\) n/a 960 4
2280.2.dn \(\chi_{2280}(217, \cdot)\) n/a 240 4
2280.2.dp \(\chi_{2280}(407, \cdot)\) None 0 4
2280.2.ds \(\chi_{2280}(197, \cdot)\) n/a 1888 4
2280.2.du \(\chi_{2280}(979, \cdot)\) n/a 1440 6
2280.2.dx \(\chi_{2280}(119, \cdot)\) None 0 6
2280.2.dy \(\chi_{2280}(941, \cdot)\) n/a 1920 6
2280.2.eb \(\chi_{2280}(61, \cdot)\) n/a 960 6
2280.2.ec \(\chi_{2280}(79, \cdot)\) None 0 6
2280.2.ef \(\chi_{2280}(41, \cdot)\) n/a 480 6
2280.2.eg \(\chi_{2280}(899, \cdot)\) n/a 2832 6
2280.2.ej \(\chi_{2280}(169, \cdot)\) n/a 360 6
2280.2.ek \(\chi_{2280}(91, \cdot)\) n/a 960 6
2280.2.en \(\chi_{2280}(29, \cdot)\) n/a 2832 6
2280.2.eo \(\chi_{2280}(671, \cdot)\) None 0 6
2280.2.er \(\chi_{2280}(751, \cdot)\) None 0 6
2280.2.es \(\chi_{2280}(709, \cdot)\) n/a 1440 6
2280.2.ev \(\chi_{2280}(131, \cdot)\) n/a 1920 6
2280.2.ew \(\chi_{2280}(89, \cdot)\) n/a 720 6
2280.2.ez \(\chi_{2280}(143, \cdot)\) None 0 12
2280.2.fa \(\chi_{2280}(557, \cdot)\) n/a 5664 12
2280.2.fd \(\chi_{2280}(97, \cdot)\) n/a 720 12
2280.2.fe \(\chi_{2280}(43, \cdot)\) n/a 2880 12
2280.2.fg \(\chi_{2280}(17, \cdot)\) n/a 1440 12
2280.2.fj \(\chi_{2280}(203, \cdot)\) n/a 5664 12
2280.2.fk \(\chi_{2280}(367, \cdot)\) None 0 12
2280.2.fn \(\chi_{2280}(13, \cdot)\) n/a 2880 12

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2280))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2280)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(190))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(228))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(285))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(380))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(456))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(570))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(760))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1140))\)\(^{\oplus 2}\)