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Properties

Label 448.3
Level 448
Weight 3
Dimension 6514
Nonzero newspaces 16
Sturm bound 36864
Trace bound 25

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Defining parameters

Level: \( N \) = \( 448 = 2^{6} \cdot 7 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(36864\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(448))\).

Total New Old
Modular forms 12720 6734 5986
Cusp forms 11856 6514 5342
Eisenstein series 864 220 644

Trace form

\( 6514 q - 32 q^{2} - 24 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 80 q^{8} - 58 q^{9} + O(q^{10}) \) \( 6514 q - 32 q^{2} - 24 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 80 q^{8} - 58 q^{9} - 32 q^{10} - 56 q^{11} - 32 q^{12} - 64 q^{13} - 40 q^{14} - 56 q^{15} - 32 q^{16} - 24 q^{17} - 32 q^{18} + 40 q^{19} - 32 q^{20} + 44 q^{21} + 64 q^{22} + 100 q^{23} + 528 q^{24} + 202 q^{25} + 368 q^{26} + 108 q^{27} + 80 q^{28} - 16 q^{29} + 128 q^{30} - 4 q^{31} - 112 q^{32} - 188 q^{33} - 272 q^{34} - 128 q^{35} - 880 q^{36} - 384 q^{37} - 592 q^{38} - 412 q^{39} - 752 q^{40} - 552 q^{41} - 480 q^{42} - 284 q^{43} - 240 q^{44} - 328 q^{45} - 32 q^{46} - 20 q^{47} - 32 q^{48} - 38 q^{49} - 704 q^{50} + 1060 q^{51} - 1088 q^{52} + 256 q^{53} - 1184 q^{54} + 1520 q^{55} - 432 q^{56} + 376 q^{57} - 752 q^{58} + 904 q^{59} - 608 q^{60} + 192 q^{61} - 64 q^{62} - 36 q^{63} + 112 q^{64} - 276 q^{65} + 480 q^{66} - 1112 q^{67} + 448 q^{68} - 440 q^{69} + 632 q^{70} - 1600 q^{71} + 1264 q^{72} - 552 q^{73} + 1200 q^{74} - 2032 q^{75} + 1632 q^{76} + 108 q^{77} + 2176 q^{78} - 1044 q^{79} + 2704 q^{80} + 878 q^{81} + 2048 q^{82} + 616 q^{83} + 1192 q^{84} + 848 q^{85} + 1840 q^{86} + 868 q^{87} + 1088 q^{88} + 1048 q^{89} + 1408 q^{90} + 748 q^{91} + 832 q^{92} + 1552 q^{93} + 160 q^{94} + 1148 q^{95} - 304 q^{96} + 904 q^{97} - 448 q^{98} + 788 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(448))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
448.3.c \(\chi_{448}(321, \cdot)\) 448.3.c.a 1 1
448.3.c.b 1
448.3.c.c 2
448.3.c.d 2
448.3.c.e 4
448.3.c.f 4
448.3.c.g 8
448.3.c.h 8
448.3.d \(\chi_{448}(127, \cdot)\) 448.3.d.a 2 1
448.3.d.b 4
448.3.d.c 4
448.3.d.d 6
448.3.d.e 8
448.3.g \(\chi_{448}(351, \cdot)\) 448.3.g.a 4 1
448.3.g.b 4
448.3.g.c 16
448.3.h \(\chi_{448}(97, \cdot)\) 448.3.h.a 8 1
448.3.h.b 24
448.3.k \(\chi_{448}(15, \cdot)\) 448.3.k.a 48 2
448.3.l \(\chi_{448}(209, \cdot)\) 448.3.l.a 4 2
448.3.l.b 56
448.3.n \(\chi_{448}(33, \cdot)\) 448.3.n.a 20 2
448.3.n.b 20
448.3.n.c 24
448.3.o \(\chi_{448}(95, \cdot)\) 448.3.o.a 20 2
448.3.o.b 20
448.3.o.c 24
448.3.r \(\chi_{448}(191, \cdot)\) 448.3.r.a 4 2
448.3.r.b 4
448.3.r.c 4
448.3.r.d 6
448.3.r.e 6
448.3.r.f 12
448.3.r.g 12
448.3.r.h 12
448.3.s \(\chi_{448}(129, \cdot)\) 448.3.s.a 2 2
448.3.s.b 2
448.3.s.c 4
448.3.s.d 4
448.3.s.e 8
448.3.s.f 8
448.3.s.g 16
448.3.s.h 16
448.3.v \(\chi_{448}(41, \cdot)\) None 0 4
448.3.w \(\chi_{448}(71, \cdot)\) None 0 4
448.3.y \(\chi_{448}(79, \cdot)\) n/a 120 4
448.3.bb \(\chi_{448}(17, \cdot)\) n/a 120 4
448.3.be \(\chi_{448}(43, \cdot)\) n/a 768 8
448.3.bf \(\chi_{448}(13, \cdot)\) n/a 1008 8
448.3.bg \(\chi_{448}(73, \cdot)\) None 0 8
448.3.bj \(\chi_{448}(23, \cdot)\) None 0 8
448.3.bk \(\chi_{448}(5, \cdot)\) n/a 2016 16
448.3.bl \(\chi_{448}(11, \cdot)\) n/a 2016 16

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(448))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(448)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 7}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 2}\)