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Properties

Label 784.5
Level 784
Weight 5
Dimension 40408
Nonzero newspaces 16
Sturm bound 188160
Trace bound 3

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Defining parameters

Level: \( N \) = \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(188160\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(784))\).

Total New Old
Modular forms 76104 40844 35260
Cusp forms 74424 40408 34016
Eisenstein series 1680 436 1244

Trace form

\( 40408 q - 62 q^{2} - 47 q^{3} - 68 q^{4} - 41 q^{5} + 4 q^{6} - 54 q^{7} - 200 q^{8} - 237 q^{9} + O(q^{10}) \) \( 40408 q - 62 q^{2} - 47 q^{3} - 68 q^{4} - 41 q^{5} + 4 q^{6} - 54 q^{7} - 200 q^{8} - 237 q^{9} - 160 q^{10} + 49 q^{11} - 392 q^{12} + 273 q^{13} - 72 q^{14} - 81 q^{15} - 228 q^{16} - 391 q^{17} + 1330 q^{18} - 3247 q^{19} + 1840 q^{20} + 342 q^{21} + 792 q^{22} + 5423 q^{23} - 1932 q^{24} + 3799 q^{25} - 3476 q^{26} - 1703 q^{27} - 72 q^{28} - 4709 q^{29} - 3800 q^{30} - 8877 q^{31} + 3148 q^{32} - 5323 q^{33} + 7448 q^{34} - 918 q^{35} + 11360 q^{36} + 5399 q^{37} + 3508 q^{38} + 12629 q^{39} - 5204 q^{40} + 303 q^{41} + 15480 q^{42} + 9965 q^{43} + 20152 q^{44} + 7425 q^{45} - 17256 q^{46} - 8685 q^{47} - 72132 q^{48} - 18018 q^{49} - 43122 q^{50} - 23697 q^{51} - 41168 q^{52} - 18953 q^{53} - 25228 q^{54} - 11795 q^{55} + 9252 q^{56} + 31077 q^{57} + 33412 q^{58} + 16753 q^{59} + 129620 q^{60} + 46935 q^{61} + 101868 q^{62} + 14826 q^{63} + 86764 q^{64} + 29303 q^{65} + 59128 q^{66} - 19791 q^{67} - 33508 q^{68} - 86645 q^{69} - 61272 q^{70} - 3733 q^{71} - 116072 q^{72} + 8693 q^{73} - 23840 q^{74} + 88079 q^{75} - 24056 q^{76} + 33894 q^{77} - 8160 q^{78} + 47667 q^{79} + 1324 q^{80} + 24707 q^{81} + 15956 q^{82} - 17321 q^{83} - 72 q^{84} - 26595 q^{85} - 4856 q^{86} - 118071 q^{87} + 7228 q^{88} - 65355 q^{89} - 36580 q^{90} - 3687 q^{91} - 95452 q^{92} - 23339 q^{93} - 246876 q^{94} + 130419 q^{95} - 112796 q^{96} - 1976 q^{97} + 29412 q^{98} - 78514 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(784))\)

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
784.5.c \(\chi_{784}(97, \cdot)\) 784.5.c.a 4 1
784.5.c.b 4
784.5.c.c 4
784.5.c.d 4
784.5.c.e 6
784.5.c.f 8
784.5.c.g 8
784.5.c.h 12
784.5.c.i 12
784.5.c.j 16
784.5.d \(\chi_{784}(687, \cdot)\) 784.5.d.a 2 1
784.5.d.b 2
784.5.d.c 2
784.5.d.d 4
784.5.d.e 4
784.5.d.f 4
784.5.d.g 6
784.5.d.h 6
784.5.d.i 8
784.5.d.j 8
784.5.d.k 10
784.5.d.l 10
784.5.d.m 16
784.5.g \(\chi_{784}(295, \cdot)\) None 0 1
784.5.h \(\chi_{784}(489, \cdot)\) None 0 1
784.5.k \(\chi_{784}(99, \cdot)\) n/a 646 2
784.5.l \(\chi_{784}(293, \cdot)\) n/a 632 2
784.5.n \(\chi_{784}(313, \cdot)\) None 0 2
784.5.o \(\chi_{784}(263, \cdot)\) None 0 2
784.5.r \(\chi_{784}(79, \cdot)\) n/a 160 2
784.5.s \(\chi_{784}(129, \cdot)\) n/a 156 2
784.5.v \(\chi_{784}(67, \cdot)\) n/a 1264 4
784.5.y \(\chi_{784}(117, \cdot)\) n/a 1264 4
784.5.z \(\chi_{784}(41, \cdot)\) None 0 6
784.5.ba \(\chi_{784}(71, \cdot)\) None 0 6
784.5.bd \(\chi_{784}(15, \cdot)\) n/a 672 6
784.5.be \(\chi_{784}(209, \cdot)\) n/a 666 6
784.5.bi \(\chi_{784}(13, \cdot)\) n/a 5352 12
784.5.bj \(\chi_{784}(43, \cdot)\) n/a 5352 12
784.5.bm \(\chi_{784}(17, \cdot)\) n/a 1332 12
784.5.bn \(\chi_{784}(95, \cdot)\) n/a 1344 12
784.5.bq \(\chi_{784}(23, \cdot)\) None 0 12
784.5.br \(\chi_{784}(73, \cdot)\) None 0 12
784.5.bs \(\chi_{784}(5, \cdot)\) n/a 10704 24
784.5.bv \(\chi_{784}(11, \cdot)\) n/a 10704 24

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(784))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(784)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 9}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 10}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 5}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(392))\)\(^{\oplus 2}\)