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Properties

Label 320.6
Level 320
Weight 6
Dimension 7854
Nonzero newspaces 14
Sturm bound 36864
Trace bound 12

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Defining parameters

Level: \( N \) = \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 14 \)
Sturm bound: \(36864\)
Trace bound: \(12\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(320))\).

Total New Old
Modular forms 15648 7986 7662
Cusp forms 15072 7854 7218
Eisenstein series 576 132 444

Trace form

\( 7854 q - 16 q^{2} - 12 q^{3} - 16 q^{4} - 24 q^{5} - 48 q^{6} - 8 q^{7} - 16 q^{8} + 466 q^{9} + O(q^{10}) \) \( 7854 q - 16 q^{2} - 12 q^{3} - 16 q^{4} - 24 q^{5} - 48 q^{6} - 8 q^{7} - 16 q^{8} + 466 q^{9} - 24 q^{10} - 1244 q^{11} - 16 q^{12} + 448 q^{13} - 16 q^{14} + 1780 q^{15} - 48 q^{16} + 1588 q^{17} - 16 q^{18} - 4732 q^{19} - 24 q^{20} - 10488 q^{21} - 27200 q^{22} - 8 q^{23} + 44064 q^{24} + 12434 q^{25} + 51872 q^{26} + 8424 q^{27} - 8736 q^{28} - 16304 q^{29} - 64904 q^{30} - 23120 q^{31} - 74336 q^{32} - 44416 q^{33} - 25536 q^{34} + 8620 q^{35} + 124592 q^{36} + 46880 q^{37} + 139264 q^{38} - 16 q^{39} + 62336 q^{40} - 26684 q^{41} - 92736 q^{42} - 30772 q^{43} - 131040 q^{44} + 23500 q^{45} - 48 q^{46} + 88344 q^{47} - 16 q^{48} + 24886 q^{49} + 137040 q^{50} - 89048 q^{51} - 146992 q^{52} - 77728 q^{53} - 466576 q^{54} + 220080 q^{55} - 301888 q^{56} - 72672 q^{57} - 52000 q^{58} - 175316 q^{59} + 197832 q^{60} + 100256 q^{61} + 350736 q^{62} - 793800 q^{63} + 749744 q^{64} - 155296 q^{65} + 509200 q^{66} - 216556 q^{67} + 14288 q^{68} + 283112 q^{69} - 286968 q^{70} + 863008 q^{71} - 828160 q^{72} + 250540 q^{73} - 755456 q^{74} + 291984 q^{75} - 537008 q^{76} - 375480 q^{77} - 665344 q^{78} - 1315728 q^{79} + 299840 q^{80} - 306266 q^{81} + 1006224 q^{82} + 202788 q^{83} + 1970064 q^{84} + 312224 q^{85} + 1443680 q^{86} + 564360 q^{87} + 446544 q^{88} + 331468 q^{89} - 284424 q^{90} + 196520 q^{91} - 1842560 q^{92} + 8768 q^{93} - 1642576 q^{94} - 327252 q^{95} - 2428736 q^{96} - 1673788 q^{97} - 1914624 q^{98} - 1069828 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(320))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
320.6.a \(\chi_{320}(1, \cdot)\) 320.6.a.a 1 1
320.6.a.b 1
320.6.a.c 1
320.6.a.d 1
320.6.a.e 1
320.6.a.f 1
320.6.a.g 1
320.6.a.h 1
320.6.a.i 1
320.6.a.j 1
320.6.a.k 1
320.6.a.l 1
320.6.a.m 1
320.6.a.n 1
320.6.a.o 1
320.6.a.p 1
320.6.a.q 2
320.6.a.r 2
320.6.a.s 2
320.6.a.t 2
320.6.a.u 2
320.6.a.v 2
320.6.a.w 2
320.6.a.x 3
320.6.a.y 3
320.6.a.z 4
320.6.c \(\chi_{320}(129, \cdot)\) 320.6.c.a 2 1
320.6.c.b 2
320.6.c.c 2
320.6.c.d 2
320.6.c.e 2
320.6.c.f 2
320.6.c.g 2
320.6.c.h 4
320.6.c.i 8
320.6.c.j 8
320.6.c.k 12
320.6.c.l 12
320.6.d \(\chi_{320}(161, \cdot)\) 320.6.d.a 8 1
320.6.d.b 8
320.6.d.c 12
320.6.d.d 12
320.6.f \(\chi_{320}(289, \cdot)\) 320.6.f.a 4 1
320.6.f.b 8
320.6.f.c 16
320.6.f.d 32
320.6.j \(\chi_{320}(47, \cdot)\) n/a 116 2
320.6.l \(\chi_{320}(81, \cdot)\) 320.6.l.a 80 2
320.6.n \(\chi_{320}(63, \cdot)\) n/a 116 2
320.6.o \(\chi_{320}(223, \cdot)\) n/a 120 2
320.6.q \(\chi_{320}(49, \cdot)\) n/a 116 2
320.6.s \(\chi_{320}(207, \cdot)\) n/a 116 2
320.6.u \(\chi_{320}(87, \cdot)\) None 0 4
320.6.x \(\chi_{320}(41, \cdot)\) None 0 4
320.6.z \(\chi_{320}(9, \cdot)\) None 0 4
320.6.ba \(\chi_{320}(7, \cdot)\) None 0 4
320.6.bd \(\chi_{320}(43, \cdot)\) n/a 1904 8
320.6.be \(\chi_{320}(21, \cdot)\) n/a 1280 8
320.6.bf \(\chi_{320}(29, \cdot)\) n/a 1904 8
320.6.bj \(\chi_{320}(3, \cdot)\) n/a 1904 8

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(320))\) into lower level spaces

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