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Properties

Label 2432.2
Level 2432
Weight 2
Dimension 102288
Nonzero newspaces 30
Sturm bound 737280
Trace bound 49

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Defining parameters

Level: \( N \) = \( 2432 = 2^{7} \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 30 \)
Sturm bound: \(737280\)
Trace bound: \(49\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2432))\).

Total New Old
Modular forms 187200 103920 83280
Cusp forms 181441 102288 79153
Eisenstein series 5759 1632 4127

Trace form

\( 102288 q - 256 q^{2} - 192 q^{3} - 256 q^{4} - 256 q^{5} - 256 q^{6} - 192 q^{7} - 256 q^{8} - 320 q^{9} + O(q^{10}) \) \( 102288 q - 256 q^{2} - 192 q^{3} - 256 q^{4} - 256 q^{5} - 256 q^{6} - 192 q^{7} - 256 q^{8} - 320 q^{9} - 256 q^{10} - 192 q^{11} - 256 q^{12} - 256 q^{13} - 256 q^{14} - 184 q^{15} - 256 q^{16} - 384 q^{17} - 256 q^{18} - 204 q^{19} - 544 q^{20} - 232 q^{21} - 256 q^{22} - 176 q^{23} - 256 q^{24} - 288 q^{25} - 256 q^{26} - 144 q^{27} - 256 q^{28} - 224 q^{29} - 256 q^{30} - 152 q^{31} - 256 q^{32} - 448 q^{33} - 256 q^{34} - 144 q^{35} - 256 q^{36} - 224 q^{37} - 272 q^{38} - 360 q^{39} - 256 q^{40} - 288 q^{41} - 256 q^{42} - 176 q^{43} - 256 q^{44} - 264 q^{45} - 256 q^{46} - 184 q^{47} - 256 q^{48} - 440 q^{49} - 352 q^{50} - 200 q^{51} - 448 q^{52} - 320 q^{53} - 512 q^{54} - 256 q^{55} - 480 q^{56} - 404 q^{57} - 832 q^{58} - 256 q^{59} - 640 q^{60} - 384 q^{61} - 448 q^{62} - 312 q^{63} - 640 q^{64} - 384 q^{65} - 640 q^{66} - 272 q^{67} - 448 q^{68} - 360 q^{69} - 640 q^{70} - 256 q^{71} - 544 q^{72} - 448 q^{73} - 480 q^{74} - 216 q^{75} - 400 q^{76} - 552 q^{77} - 448 q^{78} - 184 q^{79} - 352 q^{80} - 392 q^{81} - 256 q^{82} - 112 q^{83} - 256 q^{84} - 272 q^{85} - 256 q^{86} - 80 q^{87} - 256 q^{88} - 192 q^{89} - 256 q^{90} - 96 q^{91} - 256 q^{92} - 160 q^{93} - 256 q^{94} - 144 q^{95} - 544 q^{96} - 384 q^{97} - 256 q^{98} - 88 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2432))\)

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
2432.2.a \(\chi_{2432}(1, \cdot)\) 2432.2.a.a 1 1
2432.2.a.b 1
2432.2.a.c 1
2432.2.a.d 1
2432.2.a.e 1
2432.2.a.f 1
2432.2.a.g 1
2432.2.a.h 1
2432.2.a.i 2
2432.2.a.j 2
2432.2.a.k 2
2432.2.a.l 2
2432.2.a.m 2
2432.2.a.n 2
2432.2.a.o 2
2432.2.a.p 2
2432.2.a.q 3
2432.2.a.r 3
2432.2.a.s 3
2432.2.a.t 3
2432.2.a.u 4
2432.2.a.v 4
2432.2.a.w 4
2432.2.a.x 4
2432.2.a.y 5
2432.2.a.z 5
2432.2.a.ba 5
2432.2.a.bb 5
2432.2.b \(\chi_{2432}(1215, \cdot)\) 2432.2.b.a 4 1
2432.2.b.b 8
2432.2.b.c 12
2432.2.b.d 16
2432.2.b.e 20
2432.2.b.f 20
2432.2.c \(\chi_{2432}(1217, \cdot)\) 2432.2.c.a 2 1
2432.2.c.b 2
2432.2.c.c 4
2432.2.c.d 4
2432.2.c.e 6
2432.2.c.f 6
2432.2.c.g 6
2432.2.c.h 6
2432.2.c.i 16
2432.2.c.j 20
2432.2.h \(\chi_{2432}(2431, \cdot)\) 2432.2.h.a 20 1
2432.2.h.b 20
2432.2.h.c 20
2432.2.h.d 20
2432.2.i \(\chi_{2432}(1793, \cdot)\) n/a 160 2
2432.2.k \(\chi_{2432}(609, \cdot)\) n/a 144 2
2432.2.m \(\chi_{2432}(607, \cdot)\) n/a 152 2
2432.2.n \(\chi_{2432}(255, \cdot)\) n/a 160 2
2432.2.s \(\chi_{2432}(1471, \cdot)\) n/a 160 2
2432.2.t \(\chi_{2432}(577, \cdot)\) n/a 160 2
2432.2.u \(\chi_{2432}(303, \cdot)\) n/a 312 4
2432.2.v \(\chi_{2432}(305, \cdot)\) n/a 288 4
2432.2.y \(\chi_{2432}(385, \cdot)\) n/a 480 6
2432.2.z \(\chi_{2432}(353, \cdot)\) n/a 304 4
2432.2.bb \(\chi_{2432}(31, \cdot)\) n/a 304 4
2432.2.bd \(\chi_{2432}(153, \cdot)\) None 0 8
2432.2.be \(\chi_{2432}(151, \cdot)\) None 0 8
2432.2.bj \(\chi_{2432}(321, \cdot)\) n/a 480 6
2432.2.bl \(\chi_{2432}(319, \cdot)\) n/a 480 6
2432.2.bm \(\chi_{2432}(127, \cdot)\) n/a 480 6
2432.2.bq \(\chi_{2432}(49, \cdot)\) n/a 624 8
2432.2.br \(\chi_{2432}(335, \cdot)\) n/a 624 8
2432.2.bs \(\chi_{2432}(77, \cdot)\) n/a 4608 16
2432.2.bv \(\chi_{2432}(75, \cdot)\) n/a 5088 16
2432.2.bw \(\chi_{2432}(223, \cdot)\) n/a 912 12
2432.2.by \(\chi_{2432}(161, \cdot)\) n/a 912 12
2432.2.ca \(\chi_{2432}(103, \cdot)\) None 0 16
2432.2.cb \(\chi_{2432}(121, \cdot)\) None 0 16
2432.2.ce \(\chi_{2432}(17, \cdot)\) n/a 1872 24
2432.2.cf \(\chi_{2432}(15, \cdot)\) n/a 1872 24
2432.2.cj \(\chi_{2432}(27, \cdot)\) n/a 10176 32
2432.2.ck \(\chi_{2432}(45, \cdot)\) n/a 10176 32
2432.2.co \(\chi_{2432}(9, \cdot)\) None 0 48
2432.2.cp \(\chi_{2432}(71, \cdot)\) None 0 48
2432.2.cr \(\chi_{2432}(3, \cdot)\) n/a 30528 96
2432.2.cs \(\chi_{2432}(5, \cdot)\) n/a 30528 96

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2432))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2432)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(304))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(608))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1216))\)\(^{\oplus 2}\)