↑

Properties

Label 768.6
Level 768
Weight 6
Dimension 34456
Nonzero newspaces 12
Sturm bound 196608
Trace bound 49

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 768 = 2^{8} \cdot 3 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(196608\)
Trace bound: \(49\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(768))\).

Total New Old
Modular forms 82624 34664 47960
Cusp forms 81216 34456 46760
Eisenstein series 1408 208 1200

Trace form

\( 34456 q - 24 q^{3} - 64 q^{4} - 32 q^{6} - 48 q^{7} - 40 q^{9} + O(q^{10}) \) \( 34456 q - 24 q^{3} - 64 q^{4} - 32 q^{6} - 48 q^{7} - 40 q^{9} - 64 q^{10} - 32 q^{12} - 64 q^{13} - 24 q^{15} - 64 q^{16} - 32 q^{18} - 48 q^{19} - 32 q^{21} - 64 q^{22} - 32 q^{24} - 80 q^{25} - 24 q^{27} - 64 q^{28} - 32 q^{30} - 32 q^{31} - 56 q^{33} - 64 q^{34} - 32 q^{36} - 64 q^{37} - 24 q^{39} - 64 q^{40} - 32 q^{42} - 48 q^{43} - 32 q^{45} - 64 q^{46} - 32 q^{48} + 134360 q^{49} + 41736 q^{51} - 64 q^{52} - 197824 q^{53} - 32 q^{54} - 440240 q^{55} - 103144 q^{57} - 64 q^{58} + 115840 q^{59} - 32 q^{60} + 384576 q^{61} + 126976 q^{63} - 64 q^{64} + 443008 q^{65} - 32 q^{66} + 244592 q^{67} - 89312 q^{69} - 64 q^{70} - 575360 q^{71} - 32 q^{72} - 841168 q^{73} - 386520 q^{75} - 64 q^{76} - 59584 q^{77} - 32 q^{78} + 710672 q^{79} - 48 q^{81} - 64 q^{82} - 32 q^{84} + 49936 q^{85} - 24 q^{87} - 64 q^{88} - 32 q^{90} - 48 q^{91} - 3920 q^{93} - 64 q^{94} - 32 q^{96} - 112 q^{97} - 24 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(768))\)

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
768.6.a \(\chi_{768}(1, \cdot)\) 768.6.a.a 1 1
768.6.a.b 1
768.6.a.c 1
768.6.a.d 1
768.6.a.e 1
768.6.a.f 1
768.6.a.g 1
768.6.a.h 1
768.6.a.i 1
768.6.a.j 1
768.6.a.k 1
768.6.a.l 1
768.6.a.m 2
768.6.a.n 2
768.6.a.o 2
768.6.a.p 2
768.6.a.q 2
768.6.a.r 2
768.6.a.s 2
768.6.a.t 2
768.6.a.u 2
768.6.a.v 2
768.6.a.w 4
768.6.a.x 4
768.6.a.y 4
768.6.a.z 4
768.6.a.ba 5
768.6.a.bb 5
768.6.a.bc 5
768.6.a.bd 5
768.6.a.be 6
768.6.a.bf 6
768.6.c \(\chi_{768}(767, \cdot)\) n/a 156 1
768.6.d \(\chi_{768}(385, \cdot)\) 768.6.d.a 2 1
768.6.d.b 2
768.6.d.c 2
768.6.d.d 2
768.6.d.e 2
768.6.d.f 2
768.6.d.g 2
768.6.d.h 2
768.6.d.i 2
768.6.d.j 2
768.6.d.k 2
768.6.d.l 2
768.6.d.m 2
768.6.d.n 2
768.6.d.o 2
768.6.d.p 2
768.6.d.q 2
768.6.d.r 2
768.6.d.s 4
768.6.d.t 4
768.6.d.u 4
768.6.d.v 4
768.6.d.w 4
768.6.d.x 4
768.6.d.y 4
768.6.d.z 4
768.6.d.ba 6
768.6.d.bb 6
768.6.f \(\chi_{768}(383, \cdot)\) n/a 156 1
768.6.j \(\chi_{768}(193, \cdot)\) n/a 160 2
768.6.k \(\chi_{768}(191, \cdot)\) n/a 320 2
768.6.n \(\chi_{768}(97, \cdot)\) n/a 320 4
768.6.o \(\chi_{768}(95, \cdot)\) n/a 624 4
768.6.r \(\chi_{768}(49, \cdot)\) n/a 640 8
768.6.s \(\chi_{768}(47, \cdot)\) n/a 1264 8
768.6.v \(\chi_{768}(25, \cdot)\) None 0 16
768.6.w \(\chi_{768}(23, \cdot)\) None 0 16
768.6.z \(\chi_{768}(13, \cdot)\) n/a 10240 32
768.6.ba \(\chi_{768}(11, \cdot)\) n/a 20416 32

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(768))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(768)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 14}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 7}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(256))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(384))\)\(^{\oplus 2}\)