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Properties

Label 320.4
Level 320
Weight 4
Dimension 4686
Nonzero newspaces 14
Sturm bound 24576
Trace bound 12

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Defining parameters

Level: \( N \) = \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 14 \)
Sturm bound: \(24576\)
Trace bound: \(12\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(320))\).

Total New Old
Modular forms 9504 4818 4686
Cusp forms 8928 4686 4242
Eisenstein series 576 132 444

Trace form

\( 4686 q - 16 q^{2} - 12 q^{3} - 16 q^{4} - 24 q^{5} - 48 q^{6} - 8 q^{7} - 16 q^{8} + 34 q^{9} + O(q^{10}) \) \( 4686 q - 16 q^{2} - 12 q^{3} - 16 q^{4} - 24 q^{5} - 48 q^{6} - 8 q^{7} - 16 q^{8} + 34 q^{9} - 24 q^{10} + 4 q^{11} - 16 q^{12} - 160 q^{13} - 16 q^{14} - 140 q^{15} - 48 q^{16} - 236 q^{17} - 16 q^{18} - 60 q^{19} - 24 q^{20} - 24 q^{21} - 960 q^{22} - 8 q^{23} - 2016 q^{24} - 206 q^{25} + 32 q^{26} + 360 q^{27} + 1504 q^{28} + 784 q^{29} + 2296 q^{30} + 688 q^{31} + 2464 q^{32} + 1952 q^{33} + 1984 q^{34} + 460 q^{35} + 1712 q^{36} + 1024 q^{37} - 896 q^{38} - 16 q^{39} - 1664 q^{40} - 2108 q^{41} - 6336 q^{42} - 1684 q^{43} - 2016 q^{44} - 1508 q^{45} - 48 q^{46} - 1896 q^{47} - 16 q^{48} - 2154 q^{49} + 2832 q^{50} - 8984 q^{51} + 6608 q^{52} - 832 q^{53} + 3440 q^{54} - 592 q^{55} - 832 q^{56} + 1920 q^{57} - 4768 q^{58} + 8908 q^{59} - 4920 q^{60} + 2112 q^{61} - 6000 q^{62} + 12600 q^{63} - 12112 q^{64} - 1984 q^{65} - 11120 q^{66} + 8340 q^{67} - 4144 q^{68} - 1720 q^{69} - 2040 q^{70} + 1312 q^{71} + 1280 q^{72} + 300 q^{73} + 5248 q^{74} - 528 q^{75} + 11856 q^{76} + 744 q^{77} + 3968 q^{78} - 13840 q^{79} - 4288 q^{80} - 3866 q^{81} - 13936 q^{82} + 228 q^{83} - 8304 q^{84} + 3024 q^{85} + 992 q^{86} + 2568 q^{87} + 6224 q^{88} + 6412 q^{89} + 9336 q^{90} + 3240 q^{91} + 25216 q^{92} + 6848 q^{93} + 17840 q^{94} - 852 q^{95} + 25792 q^{96} + 11428 q^{97} + 24192 q^{98} + 3644 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(320))\)

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
320.4.a \(\chi_{320}(1, \cdot)\) 320.4.a.a 1 1
320.4.a.b 1
320.4.a.c 1
320.4.a.d 1
320.4.a.e 1
320.4.a.f 1
320.4.a.g 1
320.4.a.h 1
320.4.a.i 1
320.4.a.j 1
320.4.a.k 1
320.4.a.l 1
320.4.a.m 1
320.4.a.n 1
320.4.a.o 2
320.4.a.p 2
320.4.a.q 2
320.4.a.r 2
320.4.a.s 2
320.4.c \(\chi_{320}(129, \cdot)\) 320.4.c.a 2 1
320.4.c.b 2
320.4.c.c 2
320.4.c.d 2
320.4.c.e 2
320.4.c.f 4
320.4.c.g 4
320.4.c.h 4
320.4.c.i 4
320.4.c.j 8
320.4.d \(\chi_{320}(161, \cdot)\) 320.4.d.a 4 1
320.4.d.b 4
320.4.d.c 8
320.4.d.d 8
320.4.f \(\chi_{320}(289, \cdot)\) 320.4.f.a 4 1
320.4.f.b 8
320.4.f.c 24
320.4.j \(\chi_{320}(47, \cdot)\) 320.4.j.a 68 2
320.4.l \(\chi_{320}(81, \cdot)\) 320.4.l.a 48 2
320.4.n \(\chi_{320}(63, \cdot)\) 320.4.n.a 2 2
320.4.n.b 2
320.4.n.c 2
320.4.n.d 2
320.4.n.e 4
320.4.n.f 8
320.4.n.g 8
320.4.n.h 8
320.4.n.i 8
320.4.n.j 12
320.4.n.k 12
320.4.o \(\chi_{320}(223, \cdot)\) 320.4.o.a 12 2
320.4.o.b 12
320.4.o.c 24
320.4.o.d 24
320.4.q \(\chi_{320}(49, \cdot)\) 320.4.q.a 68 2
320.4.s \(\chi_{320}(207, \cdot)\) 320.4.s.a 68 2
320.4.u \(\chi_{320}(87, \cdot)\) None 0 4
320.4.x \(\chi_{320}(41, \cdot)\) None 0 4
320.4.z \(\chi_{320}(9, \cdot)\) None 0 4
320.4.ba \(\chi_{320}(7, \cdot)\) None 0 4
320.4.bd \(\chi_{320}(43, \cdot)\) n/a 1136 8
320.4.be \(\chi_{320}(21, \cdot)\) n/a 768 8
320.4.bf \(\chi_{320}(29, \cdot)\) n/a 1136 8
320.4.bj \(\chi_{320}(3, \cdot)\) n/a 1136 8

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(320))\) into lower level spaces

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