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Properties

Label 2592.2
Level 2592
Weight 2
Dimension 82384
Nonzero newspaces 24
Sturm bound 746496
Trace bound 89

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Defining parameters

Level: \( N \) = \( 2592 = 2^{5} \cdot 3^{4} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(746496\)
Trace bound: \(89\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2592))\).

Total New Old
Modular forms 190080 83504 106576
Cusp forms 183169 82384 100785
Eisenstein series 6911 1120 5791

Trace form

\( 82384 q - 96 q^{2} - 108 q^{3} - 160 q^{4} - 96 q^{5} - 144 q^{6} - 120 q^{7} - 96 q^{8} - 216 q^{9} + O(q^{10}) \) \( 82384 q - 96 q^{2} - 108 q^{3} - 160 q^{4} - 96 q^{5} - 144 q^{6} - 120 q^{7} - 96 q^{8} - 216 q^{9} - 232 q^{10} - 72 q^{11} - 144 q^{12} - 160 q^{13} - 96 q^{14} - 108 q^{15} - 160 q^{16} - 48 q^{17} - 144 q^{18} - 174 q^{19} - 96 q^{20} - 144 q^{21} - 160 q^{22} - 72 q^{23} - 144 q^{24} - 240 q^{25} - 96 q^{26} - 108 q^{27} - 232 q^{28} - 96 q^{29} - 144 q^{30} - 120 q^{31} - 96 q^{32} - 360 q^{33} - 160 q^{34} - 78 q^{35} - 144 q^{36} - 232 q^{37} - 96 q^{38} - 108 q^{39} - 160 q^{40} - 144 q^{41} - 144 q^{42} - 120 q^{43} - 96 q^{44} - 144 q^{45} - 232 q^{46} - 72 q^{47} - 144 q^{48} - 80 q^{49} - 96 q^{50} - 108 q^{51} - 160 q^{52} - 96 q^{53} - 144 q^{54} - 194 q^{55} - 96 q^{56} - 216 q^{57} - 160 q^{58} - 108 q^{59} - 144 q^{60} - 208 q^{61} - 96 q^{62} - 108 q^{63} - 232 q^{64} - 336 q^{65} - 144 q^{66} - 168 q^{67} - 96 q^{68} - 144 q^{69} - 160 q^{70} - 150 q^{71} - 144 q^{72} - 396 q^{73} - 96 q^{74} - 108 q^{75} - 160 q^{76} - 192 q^{77} - 144 q^{78} - 168 q^{79} - 96 q^{80} - 72 q^{81} - 448 q^{82} - 132 q^{83} - 144 q^{84} - 208 q^{85} - 96 q^{86} - 108 q^{87} - 160 q^{88} - 168 q^{89} - 144 q^{90} - 202 q^{91} - 96 q^{92} - 144 q^{93} - 128 q^{94} - 102 q^{95} - 144 q^{96} - 400 q^{97} - 96 q^{98} - 108 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2592))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
2592.2.a \(\chi_{2592}(1, \cdot)\) 2592.2.a.a 1 1
2592.2.a.b 1
2592.2.a.c 1
2592.2.a.d 1
2592.2.a.e 1
2592.2.a.f 1
2592.2.a.g 1
2592.2.a.h 1
2592.2.a.i 2
2592.2.a.j 2
2592.2.a.k 2
2592.2.a.l 2
2592.2.a.m 2
2592.2.a.n 2
2592.2.a.o 2
2592.2.a.p 2
2592.2.a.q 2
2592.2.a.r 2
2592.2.a.s 2
2592.2.a.t 2
2592.2.a.u 4
2592.2.a.v 4
2592.2.a.w 4
2592.2.a.x 4
2592.2.c \(\chi_{2592}(2591, \cdot)\) 2592.2.c.a 8 1
2592.2.c.b 16
2592.2.c.c 24
2592.2.d \(\chi_{2592}(1297, \cdot)\) 2592.2.d.a 2 1
2592.2.d.b 2
2592.2.d.c 2
2592.2.d.d 2
2592.2.d.e 4
2592.2.d.f 4
2592.2.d.g 4
2592.2.d.h 4
2592.2.d.i 4
2592.2.d.j 8
2592.2.d.k 8
2592.2.f \(\chi_{2592}(1295, \cdot)\) 2592.2.f.a 4 1
2592.2.f.b 16
2592.2.f.c 24
2592.2.i \(\chi_{2592}(865, \cdot)\) 2592.2.i.a 2 2
2592.2.i.b 2
2592.2.i.c 2
2592.2.i.d 2
2592.2.i.e 2
2592.2.i.f 2
2592.2.i.g 2
2592.2.i.h 2
2592.2.i.i 2
2592.2.i.j 2
2592.2.i.k 2
2592.2.i.l 2
2592.2.i.m 2
2592.2.i.n 2
2592.2.i.o 2
2592.2.i.p 2
2592.2.i.q 2
2592.2.i.r 2
2592.2.i.s 2
2592.2.i.t 2
2592.2.i.u 2
2592.2.i.v 2
2592.2.i.w 2
2592.2.i.x 2
2592.2.i.y 4
2592.2.i.z 4
2592.2.i.ba 4
2592.2.i.bb 4
2592.2.i.bc 4
2592.2.i.bd 4
2592.2.i.be 4
2592.2.i.bf 4
2592.2.i.bg 8
2592.2.i.bh 8
2592.2.k \(\chi_{2592}(649, \cdot)\) None 0 2
2592.2.l \(\chi_{2592}(647, \cdot)\) None 0 2
2592.2.p \(\chi_{2592}(431, \cdot)\) 2592.2.p.a 4 2
2592.2.p.b 4
2592.2.p.c 4
2592.2.p.d 8
2592.2.p.e 8
2592.2.p.f 16
2592.2.p.g 48
2592.2.r \(\chi_{2592}(433, \cdot)\) 2592.2.r.a 4 2
2592.2.r.b 4
2592.2.r.c 4
2592.2.r.d 4
2592.2.r.e 4
2592.2.r.f 4
2592.2.r.g 4
2592.2.r.h 4
2592.2.r.i 4
2592.2.r.j 4
2592.2.r.k 4
2592.2.r.l 4
2592.2.r.m 4
2592.2.r.n 8
2592.2.r.o 8
2592.2.r.p 8
2592.2.r.q 16
2592.2.s \(\chi_{2592}(863, \cdot)\) 2592.2.s.a 8 2
2592.2.s.b 8
2592.2.s.c 8
2592.2.s.d 8
2592.2.s.e 8
2592.2.s.f 8
2592.2.s.g 8
2592.2.s.h 8
2592.2.s.i 16
2592.2.s.j 16
2592.2.v \(\chi_{2592}(325, \cdot)\) n/a 752 4
2592.2.w \(\chi_{2592}(323, \cdot)\) n/a 752 4
2592.2.y \(\chi_{2592}(289, \cdot)\) n/a 216 6
2592.2.z \(\chi_{2592}(215, \cdot)\) None 0 4
2592.2.bc \(\chi_{2592}(217, \cdot)\) None 0 4
2592.2.bf \(\chi_{2592}(145, \cdot)\) n/a 204 6
2592.2.bh \(\chi_{2592}(143, \cdot)\) n/a 204 6
2592.2.bi \(\chi_{2592}(287, \cdot)\) n/a 216 6
2592.2.bk \(\chi_{2592}(109, \cdot)\) n/a 1520 8
2592.2.bn \(\chi_{2592}(107, \cdot)\) n/a 1520 8
2592.2.bo \(\chi_{2592}(97, \cdot)\) n/a 1944 18
2592.2.bp \(\chi_{2592}(73, \cdot)\) None 0 12
2592.2.bs \(\chi_{2592}(71, \cdot)\) None 0 12
2592.2.bv \(\chi_{2592}(47, \cdot)\) n/a 1908 18
2592.2.bx \(\chi_{2592}(49, \cdot)\) n/a 1908 18
2592.2.by \(\chi_{2592}(95, \cdot)\) n/a 1944 18
2592.2.cb \(\chi_{2592}(35, \cdot)\) n/a 3408 24
2592.2.cc \(\chi_{2592}(37, \cdot)\) n/a 3408 24
2592.2.ce \(\chi_{2592}(23, \cdot)\) None 0 36
2592.2.ch \(\chi_{2592}(25, \cdot)\) None 0 36
2592.2.ci \(\chi_{2592}(11, \cdot)\) n/a 30960 72
2592.2.cl \(\chi_{2592}(13, \cdot)\) n/a 30960 72

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2592))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2592)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(324))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(432))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(648))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(864))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1296))\)\(^{\oplus 2}\)