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Properties

Label 928.4
Level 928
Weight 4
Dimension 44982
Nonzero newspaces 20
Sturm bound 215040
Trace bound 9

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Defining parameters

Level: \( N \) = \( 928 = 2^{5} \cdot 29 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(215040\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(928))\).

Total New Old
Modular forms 81536 45522 36014
Cusp forms 79744 44982 34762
Eisenstein series 1792 540 1252

Trace form

\( 44982 q - 104 q^{2} - 76 q^{3} - 104 q^{4} - 108 q^{5} - 104 q^{6} - 108 q^{7} - 104 q^{8} - 250 q^{9} + O(q^{10}) \) \( 44982 q - 104 q^{2} - 76 q^{3} - 104 q^{4} - 108 q^{5} - 104 q^{6} - 108 q^{7} - 104 q^{8} - 250 q^{9} - 344 q^{10} - 76 q^{11} - 8 q^{12} + 132 q^{13} + 312 q^{14} + 140 q^{15} + 496 q^{16} + 308 q^{17} + 256 q^{18} - 76 q^{19} - 264 q^{20} - 616 q^{21} - 496 q^{22} - 1340 q^{23} - 16 q^{24} - 830 q^{25} - 144 q^{26} + 452 q^{27} - 864 q^{28} + 90 q^{29} - 2600 q^{30} + 2316 q^{31} - 1344 q^{32} + 680 q^{33} - 1168 q^{34} + 836 q^{35} - 3024 q^{36} - 1772 q^{37} - 2072 q^{38} - 2396 q^{39} + 960 q^{40} - 1060 q^{41} + 4416 q^{42} - 1692 q^{43} + 3976 q^{44} + 2348 q^{45} + 2776 q^{46} + 1260 q^{47} + 4784 q^{48} + 2094 q^{49} + 7016 q^{50} + 2684 q^{51} + 4936 q^{52} - 1004 q^{53} + 2064 q^{54} - 172 q^{55} - 2496 q^{56} - 2224 q^{57} - 3312 q^{58} - 2912 q^{59} - 11616 q^{60} + 1764 q^{61} - 6880 q^{62} - 5076 q^{63} - 10016 q^{64} - 3712 q^{65} - 12104 q^{66} - 4156 q^{67} - 5648 q^{68} + 472 q^{69} - 2912 q^{70} - 812 q^{71} + 3304 q^{72} + 1340 q^{73} + 6840 q^{74} + 3340 q^{75} + 10136 q^{76} - 1352 q^{77} + 23720 q^{78} - 1940 q^{79} + 20512 q^{80} + 2942 q^{81} + 12696 q^{82} - 4956 q^{83} + 13008 q^{84} + 1832 q^{85} + 1744 q^{86} + 2888 q^{87} - 2720 q^{88} + 3420 q^{89} - 14912 q^{90} + 7124 q^{91} - 20416 q^{92} - 10128 q^{93} - 25792 q^{94} + 10524 q^{95} - 35696 q^{96} - 4988 q^{97} - 22560 q^{98} + 10764 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(928))\)

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
928.4.a \(\chi_{928}(1, \cdot)\) 928.4.a.a 1 1
928.4.a.b 1
928.4.a.c 8
928.4.a.d 9
928.4.a.e 9
928.4.a.f 10
928.4.a.g 10
928.4.a.h 12
928.4.a.i 12
928.4.a.j 12
928.4.c \(\chi_{928}(465, \cdot)\) 928.4.c.a 84 1
928.4.e \(\chi_{928}(289, \cdot)\) 928.4.e.a 2 1
928.4.e.b 4
928.4.e.c 8
928.4.e.d 32
928.4.e.e 44
928.4.g \(\chi_{928}(753, \cdot)\) 928.4.g.a 88 1
928.4.j \(\chi_{928}(679, \cdot)\) None 0 2
928.4.k \(\chi_{928}(191, \cdot)\) n/a 180 2
928.4.m \(\chi_{928}(57, \cdot)\) None 0 2
928.4.n \(\chi_{928}(233, \cdot)\) None 0 2
928.4.q \(\chi_{928}(655, \cdot)\) n/a 176 2
928.4.t \(\chi_{928}(215, \cdot)\) None 0 2
928.4.u \(\chi_{928}(65, \cdot)\) n/a 540 6
928.4.v \(\chi_{928}(117, \cdot)\) n/a 1344 4
928.4.x \(\chi_{928}(307, \cdot)\) n/a 1432 4
928.4.ba \(\chi_{928}(75, \cdot)\) n/a 1432 4
928.4.bc \(\chi_{928}(173, \cdot)\) n/a 1432 4
928.4.be \(\chi_{928}(209, \cdot)\) n/a 528 6
928.4.bg \(\chi_{928}(33, \cdot)\) n/a 540 6
928.4.bi \(\chi_{928}(49, \cdot)\) n/a 528 6
928.4.bk \(\chi_{928}(55, \cdot)\) None 0 12
928.4.bn \(\chi_{928}(15, \cdot)\) n/a 1056 12
928.4.bq \(\chi_{928}(25, \cdot)\) None 0 12
928.4.br \(\chi_{928}(9, \cdot)\) None 0 12
928.4.bt \(\chi_{928}(31, \cdot)\) n/a 1080 12
928.4.bu \(\chi_{928}(39, \cdot)\) None 0 12
928.4.bx \(\chi_{928}(5, \cdot)\) n/a 8592 24
928.4.bz \(\chi_{928}(11, \cdot)\) n/a 8592 24
928.4.ca \(\chi_{928}(3, \cdot)\) n/a 8592 24
928.4.cc \(\chi_{928}(45, \cdot)\) n/a 8592 24

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(928))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(928)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(232))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(464))\)\(^{\oplus 2}\)