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Properties

Label 320.2
Level 320
Weight 2
Dimension 1518
Nonzero newspaces 14
Newform subspaces 42
Sturm bound 12288
Trace bound 12

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Defining parameters

Level: \( N \) = \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 14 \)
Newform subspaces: \( 42 \)
Sturm bound: \(12288\)
Trace bound: \(12\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(320))\).

Total New Old
Modular forms 3360 1650 1710
Cusp forms 2785 1518 1267
Eisenstein series 575 132 443

Trace form

\( 1518 q - 16 q^{2} - 12 q^{3} - 16 q^{4} - 24 q^{5} - 48 q^{6} - 8 q^{7} - 16 q^{8} - 14 q^{9} + O(q^{10}) \) \( 1518 q - 16 q^{2} - 12 q^{3} - 16 q^{4} - 24 q^{5} - 48 q^{6} - 8 q^{7} - 16 q^{8} - 14 q^{9} - 24 q^{10} - 28 q^{11} - 16 q^{12} - 16 q^{14} - 12 q^{15} - 48 q^{16} - 12 q^{17} - 16 q^{18} + 4 q^{19} - 24 q^{20} - 56 q^{21} - 32 q^{22} - 8 q^{23} - 96 q^{24} - 46 q^{25} - 128 q^{26} - 24 q^{27} - 96 q^{28} - 48 q^{29} - 104 q^{30} - 80 q^{31} - 96 q^{32} - 64 q^{33} - 96 q^{34} - 20 q^{35} - 208 q^{36} - 32 q^{37} - 96 q^{38} - 16 q^{39} - 64 q^{40} - 60 q^{41} - 96 q^{42} + 12 q^{43} - 32 q^{44} - 20 q^{45} - 48 q^{46} + 24 q^{47} - 16 q^{48} - 10 q^{49} - 88 q^{51} + 80 q^{52} + 32 q^{53} + 112 q^{54} - 80 q^{55} + 64 q^{56} - 32 q^{57} + 128 q^{58} - 148 q^{59} + 72 q^{60} - 32 q^{61} + 48 q^{62} - 200 q^{63} + 176 q^{64} - 96 q^{65} + 112 q^{66} - 236 q^{67} + 80 q^{68} - 88 q^{69} + 72 q^{70} - 224 q^{71} + 128 q^{72} - 84 q^{73} + 96 q^{74} - 176 q^{75} + 80 q^{76} - 120 q^{77} + 32 q^{78} - 144 q^{79} - 64 q^{80} - 218 q^{81} - 176 q^{82} - 92 q^{83} - 240 q^{84} - 128 q^{85} - 256 q^{86} - 120 q^{87} - 176 q^{88} - 180 q^{89} - 168 q^{90} - 88 q^{91} - 320 q^{92} - 192 q^{93} - 208 q^{94} - 84 q^{95} - 320 q^{96} - 124 q^{97} - 288 q^{98} - 132 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(320))\)

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
320.2.a \(\chi_{320}(1, \cdot)\) 320.2.a.a 1 1
320.2.a.b 1
320.2.a.c 1
320.2.a.d 1
320.2.a.e 1
320.2.a.f 1
320.2.a.g 2
320.2.c \(\chi_{320}(129, \cdot)\) 320.2.c.a 2 1
320.2.c.b 2
320.2.c.c 2
320.2.c.d 4
320.2.d \(\chi_{320}(161, \cdot)\) 320.2.d.a 4 1
320.2.d.b 4
320.2.f \(\chi_{320}(289, \cdot)\) 320.2.f.a 4 1
320.2.f.b 8
320.2.j \(\chi_{320}(47, \cdot)\) 320.2.j.a 2 2
320.2.j.b 18
320.2.l \(\chi_{320}(81, \cdot)\) 320.2.l.a 16 2
320.2.n \(\chi_{320}(63, \cdot)\) 320.2.n.a 2 2
320.2.n.b 2
320.2.n.c 2
320.2.n.d 2
320.2.n.e 2
320.2.n.f 2
320.2.n.g 2
320.2.n.h 2
320.2.n.i 4
320.2.o \(\chi_{320}(223, \cdot)\) 320.2.o.a 2 2
320.2.o.b 2
320.2.o.c 2
320.2.o.d 2
320.2.o.e 8
320.2.o.f 8
320.2.q \(\chi_{320}(49, \cdot)\) 320.2.q.a 2 2
320.2.q.b 2
320.2.q.c 16
320.2.s \(\chi_{320}(207, \cdot)\) 320.2.s.a 2 2
320.2.s.b 18
320.2.u \(\chi_{320}(87, \cdot)\) None 0 4
320.2.x \(\chi_{320}(41, \cdot)\) None 0 4
320.2.z \(\chi_{320}(9, \cdot)\) None 0 4
320.2.ba \(\chi_{320}(7, \cdot)\) None 0 4
320.2.bd \(\chi_{320}(43, \cdot)\) 320.2.bd.a 368 8
320.2.be \(\chi_{320}(21, \cdot)\) 320.2.be.a 256 8
320.2.bf \(\chi_{320}(29, \cdot)\) 320.2.bf.a 368 8
320.2.bj \(\chi_{320}(3, \cdot)\) 320.2.bj.a 368 8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(320))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(320)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(320))\)\(^{\oplus 1}\)