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Properties

Label 304.6
Level 304
Weight 6
Dimension 7979
Nonzero newspaces 12
Sturm bound 34560
Trace bound 7

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Defining parameters

Level: \( N \) = \( 304 = 2^{4} \cdot 19 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(34560\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(304))\).

Total New Old
Modular forms 14652 8131 6521
Cusp forms 14148 7979 6169
Eisenstein series 504 152 352

Trace form

\( 7979 q - 32 q^{2} - 7 q^{3} + 12 q^{4} - q^{5} - 260 q^{6} - 251 q^{7} - 524 q^{8} - 125 q^{9} + O(q^{10}) \) \( 7979 q - 32 q^{2} - 7 q^{3} + 12 q^{4} - q^{5} - 260 q^{6} - 251 q^{7} - 524 q^{8} - 125 q^{9} + 836 q^{10} + 2513 q^{11} - 44 q^{12} - 161 q^{13} + 164 q^{14} - 7875 q^{15} + 1708 q^{16} + 1135 q^{17} + 6240 q^{18} + 6215 q^{19} - 6016 q^{20} - 2165 q^{21} - 8876 q^{22} - 7867 q^{23} - 16772 q^{24} - 4293 q^{25} - 14772 q^{26} - 3691 q^{27} + 14636 q^{28} - 433 q^{29} + 60852 q^{30} + 20101 q^{31} + 47948 q^{32} + 7927 q^{33} + 3444 q^{34} - 23251 q^{35} - 13820 q^{36} + 1190 q^{37} - 53284 q^{38} + 29098 q^{39} - 150580 q^{40} - 16689 q^{41} - 66836 q^{42} - 11839 q^{43} + 80212 q^{44} + 22359 q^{45} + 185028 q^{46} - 43643 q^{47} + 295948 q^{48} + 79327 q^{49} + 170064 q^{50} - 56707 q^{51} - 183180 q^{52} - 111857 q^{53} - 417380 q^{54} + 39941 q^{55} - 382292 q^{56} - 50857 q^{57} - 213624 q^{58} + 77857 q^{59} + 308700 q^{60} - 23125 q^{61} + 547708 q^{62} + 214965 q^{63} + 567516 q^{64} + 440239 q^{65} + 306676 q^{66} + 625085 q^{67} - 267460 q^{68} - 51069 q^{69} - 824356 q^{70} - 259697 q^{71} - 940524 q^{72} - 608013 q^{73} - 294332 q^{74} - 919164 q^{75} + 87432 q^{76} - 523486 q^{77} + 1263524 q^{78} - 299833 q^{79} + 1108876 q^{80} + 317883 q^{81} + 186396 q^{82} + 81811 q^{83} - 381812 q^{84} + 631603 q^{85} - 940972 q^{86} + 885081 q^{87} - 1180692 q^{88} + 228135 q^{89} - 560340 q^{90} + 230037 q^{91} + 443756 q^{92} - 866401 q^{93} + 921788 q^{94} + 70241 q^{95} + 1194584 q^{96} + 146991 q^{97} + 889256 q^{98} + 525529 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(304))\)

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
304.6.a \(\chi_{304}(1, \cdot)\) 304.6.a.a 1 1
304.6.a.b 1
304.6.a.c 1
304.6.a.d 1
304.6.a.e 1
304.6.a.f 2
304.6.a.g 2
304.6.a.h 3
304.6.a.i 3
304.6.a.j 3
304.6.a.k 4
304.6.a.l 4
304.6.a.m 6
304.6.a.n 6
304.6.a.o 7
304.6.b \(\chi_{304}(151, \cdot)\) None 0 1
304.6.c \(\chi_{304}(153, \cdot)\) None 0 1
304.6.h \(\chi_{304}(303, \cdot)\) 304.6.h.a 2 1
304.6.h.b 4
304.6.h.c 16
304.6.h.d 28
304.6.i \(\chi_{304}(49, \cdot)\) 304.6.i.a 6 2
304.6.i.b 8
304.6.i.c 16
304.6.i.d 18
304.6.i.e 24
304.6.i.f 26
304.6.k \(\chi_{304}(77, \cdot)\) n/a 360 2
304.6.m \(\chi_{304}(75, \cdot)\) n/a 396 2
304.6.n \(\chi_{304}(31, \cdot)\) 304.6.n.a 32 2
304.6.n.b 32
304.6.n.c 36
304.6.s \(\chi_{304}(103, \cdot)\) None 0 2
304.6.t \(\chi_{304}(121, \cdot)\) None 0 2
304.6.u \(\chi_{304}(17, \cdot)\) n/a 294 6
304.6.v \(\chi_{304}(45, \cdot)\) n/a 792 4
304.6.x \(\chi_{304}(27, \cdot)\) n/a 792 4
304.6.bb \(\chi_{304}(9, \cdot)\) None 0 6
304.6.bd \(\chi_{304}(71, \cdot)\) None 0 6
304.6.be \(\chi_{304}(15, \cdot)\) n/a 300 6
304.6.bg \(\chi_{304}(3, \cdot)\) n/a 2376 12
304.6.bi \(\chi_{304}(5, \cdot)\) n/a 2376 12

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(304))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(304)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 2}\)