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Properties

Label 304.5
Level 304
Weight 5
Dimension 6367
Nonzero newspaces 12
Sturm bound 28800
Trace bound 7

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Defining parameters

Level: \( N \) = \( 304 = 2^{4} \cdot 19 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(28800\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(304))\).

Total New Old
Modular forms 11772 6521 5251
Cusp forms 11268 6367 4901
Eisenstein series 504 154 350

Trace form

\( 6367 q - 32 q^{2} - 23 q^{3} - 20 q^{4} - 113 q^{5} - 164 q^{6} - 19 q^{7} + 148 q^{8} + 435 q^{9} + O(q^{10}) \) \( 6367 q - 32 q^{2} - 23 q^{3} - 20 q^{4} - 113 q^{5} - 164 q^{6} - 19 q^{7} + 148 q^{8} + 435 q^{9} + 164 q^{10} - 215 q^{11} + 628 q^{12} - 753 q^{13} - 124 q^{14} - 27 q^{15} + 300 q^{16} + 431 q^{17} - 2816 q^{18} + 679 q^{19} - 3872 q^{20} - 1253 q^{21} - 1836 q^{22} - 2323 q^{23} + 3708 q^{24} + 1195 q^{25} + 6796 q^{26} + 3301 q^{27} + 7532 q^{28} + 3919 q^{29} + 7444 q^{30} - 27 q^{31} - 6452 q^{32} - 6985 q^{33} - 15052 q^{34} - 2707 q^{35} - 22972 q^{36} + 1496 q^{37} - 3604 q^{38} - 5422 q^{39} + 10252 q^{40} - 657 q^{41} + 34092 q^{42} - 3415 q^{43} + 29236 q^{44} + 5127 q^{45} + 10596 q^{46} - 27 q^{47} - 13812 q^{48} - 7977 q^{49} - 40176 q^{50} + 5997 q^{51} - 40940 q^{52} - 1457 q^{53} - 21604 q^{54} + 23533 q^{55} + 13868 q^{56} + 11127 q^{57} + 40840 q^{58} + 5545 q^{59} + 59804 q^{60} + 42303 q^{61} + 22908 q^{62} + 15525 q^{63} - 31652 q^{64} - 30457 q^{65} - 60332 q^{66} - 76503 q^{67} - 36100 q^{68} - 104837 q^{69} - 30628 q^{70} - 67171 q^{71} + 35380 q^{72} - 3937 q^{73} + 47524 q^{74} - 35176 q^{75} + 23960 q^{76} + 65150 q^{77} + 16068 q^{78} + 71541 q^{79} - 2804 q^{80} + 91583 q^{81} - 32068 q^{82} + 78601 q^{83} - 39284 q^{84} + 39531 q^{85} + 9556 q^{86} + 137421 q^{87} - 14612 q^{88} - 51057 q^{89} + 10796 q^{90} - 29203 q^{91} + 29228 q^{92} - 88829 q^{93} - 900 q^{94} - 27 q^{95} - 12200 q^{96} + 6319 q^{97} + 24456 q^{98} - 98455 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(304))\)

We only show spaces with odd 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
304.5.d \(\chi_{304}(191, \cdot)\) 304.5.d.a 12 1
304.5.d.b 24
304.5.e \(\chi_{304}(113, \cdot)\) 304.5.e.a 1 1
304.5.e.b 2
304.5.e.c 4
304.5.e.d 4
304.5.e.e 8
304.5.e.f 20
304.5.f \(\chi_{304}(39, \cdot)\) None 0 1
304.5.g \(\chi_{304}(265, \cdot)\) None 0 1
304.5.j \(\chi_{304}(37, \cdot)\) n/a 316 2
304.5.l \(\chi_{304}(115, \cdot)\) n/a 288 2
304.5.o \(\chi_{304}(7, \cdot)\) None 0 2
304.5.p \(\chi_{304}(217, \cdot)\) None 0 2
304.5.q \(\chi_{304}(159, \cdot)\) 304.5.q.a 24 2
304.5.q.b 28
304.5.q.c 28
304.5.r \(\chi_{304}(65, \cdot)\) 304.5.r.a 10 2
304.5.r.b 12
304.5.r.c 16
304.5.r.d 40
304.5.w \(\chi_{304}(69, \cdot)\) n/a 632 4
304.5.y \(\chi_{304}(11, \cdot)\) n/a 632 4
304.5.z \(\chi_{304}(33, \cdot)\) n/a 234 6
304.5.ba \(\chi_{304}(41, \cdot)\) None 0 6
304.5.bc \(\chi_{304}(23, \cdot)\) None 0 6
304.5.bf \(\chi_{304}(47, \cdot)\) n/a 240 6
304.5.bh \(\chi_{304}(35, \cdot)\) n/a 1896 12
304.5.bj \(\chi_{304}(13, \cdot)\) n/a 1896 12

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(304))\) into lower level spaces

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