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Properties

Label 384.6
Level 384
Weight 6
Dimension 8592
Nonzero newspaces 10
Sturm bound 49152
Trace bound 25

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Defining parameters

Level: \( N \) = \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 10 \)
Sturm bound: \(49152\)
Trace bound: \(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(384))\).

Total New Old
Modular forms 20800 8688 12112
Cusp forms 20160 8592 11568
Eisenstein series 640 96 544

Trace form

\( 8592 q - 12 q^{3} - 32 q^{4} - 16 q^{6} - 24 q^{7} - 20 q^{9} + O(q^{10}) \) \( 8592 q - 12 q^{3} - 32 q^{4} - 16 q^{6} - 24 q^{7} - 20 q^{9} - 32 q^{10} - 16 q^{12} - 32 q^{13} - 8 q^{15} - 32 q^{16} - 16 q^{18} - 24 q^{19} + 956 q^{21} - 32 q^{22} + 3344 q^{23} - 16 q^{24} - 24968 q^{25} - 7476 q^{27} - 32 q^{28} + 16288 q^{29} - 16 q^{30} + 46096 q^{31} + 22656 q^{33} - 32 q^{34} - 9552 q^{35} - 16 q^{36} - 42624 q^{37} - 44916 q^{39} - 32 q^{40} - 19808 q^{41} - 16 q^{42} + 64120 q^{43} + 12484 q^{45} - 32 q^{46} - 16 q^{48} - 134504 q^{49} - 548256 q^{50} - 19920 q^{51} + 293920 q^{52} + 197824 q^{53} + 116624 q^{54} + 220072 q^{55} + 603680 q^{56} + 103084 q^{57} + 103936 q^{58} - 57920 q^{59} - 395728 q^{60} - 384672 q^{61} - 702528 q^{62} - 63536 q^{63} - 1499552 q^{64} - 443008 q^{65} - 509776 q^{66} - 122344 q^{67} - 28608 q^{68} + 88292 q^{69} + 1147744 q^{70} + 287680 q^{71} - 16 q^{72} + 841048 q^{73} + 1510880 q^{74} + 180736 q^{75} + 1073888 q^{76} + 59584 q^{77} - 389680 q^{78} - 355376 q^{79} - 1973856 q^{80} + 84808 q^{81} - 32 q^{82} - 16 q^{84} - 50032 q^{85} + 282172 q^{87} - 32 q^{88} - 16 q^{90} - 24 q^{91} - 362368 q^{93} - 32 q^{94} - 16 q^{96} - 64 q^{97} - 339532 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(384))\)

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
384.6.a \(\chi_{384}(1, \cdot)\) 384.6.a.a 1 1
384.6.a.b 1
384.6.a.c 1
384.6.a.d 1
384.6.a.e 2
384.6.a.f 2
384.6.a.g 2
384.6.a.h 2
384.6.a.i 2
384.6.a.j 2
384.6.a.k 2
384.6.a.l 2
384.6.a.m 2
384.6.a.n 2
384.6.a.o 2
384.6.a.p 2
384.6.a.q 3
384.6.a.r 3
384.6.a.s 3
384.6.a.t 3
384.6.c \(\chi_{384}(383, \cdot)\) 384.6.c.a 20 1
384.6.c.b 20
384.6.c.c 20
384.6.c.d 20
384.6.d \(\chi_{384}(193, \cdot)\) 384.6.d.a 2 1
384.6.d.b 2
384.6.d.c 2
384.6.d.d 2
384.6.d.e 2
384.6.d.f 2
384.6.d.g 4
384.6.d.h 4
384.6.d.i 8
384.6.d.j 12
384.6.f \(\chi_{384}(191, \cdot)\) 384.6.f.a 4 1
384.6.f.b 4
384.6.f.c 16
384.6.f.d 16
384.6.f.e 20
384.6.f.f 20
384.6.j \(\chi_{384}(97, \cdot)\) 384.6.j.a 40 2
384.6.j.b 40
384.6.k \(\chi_{384}(95, \cdot)\) n/a 152 2
384.6.n \(\chi_{384}(49, \cdot)\) n/a 160 4
384.6.o \(\chi_{384}(47, \cdot)\) n/a 312 4
384.6.r \(\chi_{384}(25, \cdot)\) None 0 8
384.6.s \(\chi_{384}(23, \cdot)\) None 0 8
384.6.v \(\chi_{384}(13, \cdot)\) n/a 2560 16
384.6.w \(\chi_{384}(11, \cdot)\) n/a 5088 16

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(384))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(384)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 7}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 2}\)