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

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

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

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