Properties

Label 354.8
Level 354
Weight 8
Dimension 6088
Nonzero newspaces 4
Sturm bound 55680
Trace bound 1

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Defining parameters

Level: \( N \) = \( 354 = 2 \cdot 3 \cdot 59 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(55680\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(354))\).

Total New Old
Modular forms 24592 6088 18504
Cusp forms 24128 6088 18040
Eisenstein series 464 0 464

Trace form

\( 6088 q - 16 q^{2} - 54 q^{3} - 128 q^{4} + 228 q^{5} - 432 q^{6} + 3152 q^{7} - 1024 q^{8} - 1458 q^{9} + O(q^{10}) \) \( 6088 q - 16 q^{2} - 54 q^{3} - 128 q^{4} + 228 q^{5} - 432 q^{6} + 3152 q^{7} - 1024 q^{8} - 1458 q^{9} + 1824 q^{10} - 14664 q^{11} - 3456 q^{12} + 7604 q^{13} + 25216 q^{14} + 6156 q^{15} - 8192 q^{16} + 13212 q^{17} - 11664 q^{18} - 49720 q^{19} + 14592 q^{20} + 85104 q^{21} - 117312 q^{22} - 82896 q^{23} - 27648 q^{24} + 130258 q^{25} + 60832 q^{26} - 39366 q^{27} + 201728 q^{28} + 83220 q^{29} + 49248 q^{30} - 66304 q^{31} - 65536 q^{32} - 395928 q^{33} + 105696 q^{34} - 359328 q^{35} - 93312 q^{36} + 72932 q^{37} - 397760 q^{38} + 205308 q^{39} + 116736 q^{40} + 1278156 q^{41} + 680832 q^{42} + 312824 q^{43} - 938496 q^{44} - 20876710 q^{45} + 5416160 q^{46} + 20490460 q^{47} - 221184 q^{48} + 2889478 q^{49} - 15927344 q^{50} - 31528660 q^{51} - 17278976 q^{52} - 29985892 q^{53} - 11976872 q^{54} + 10222404 q^{55} + 1613824 q^{56} + 46792630 q^{57} + 23298752 q^{58} + 42125444 q^{59} + 23768448 q^{60} + 14926572 q^{61} - 6960544 q^{62} - 45277562 q^{63} - 524288 q^{64} - 106954308 q^{65} - 63188840 q^{66} - 43158432 q^{67} - 6110720 q^{68} + 32934632 q^{69} + 85521088 q^{70} + 118182152 q^{71} - 746496 q^{72} + 27434776 q^{73} - 61454272 q^{74} - 121129036 q^{75} - 3182080 q^{76} + 23110464 q^{77} + 1642464 q^{78} - 7614880 q^{79} + 933888 q^{80} - 1062882 q^{81} + 10225248 q^{82} - 4458936 q^{83} + 5446656 q^{84} - 1506168 q^{85} + 2502592 q^{86} + 2246940 q^{87} - 7507968 q^{88} - 11982420 q^{89} + 1329696 q^{90} - 11983904 q^{91} - 5305344 q^{92} - 1790208 q^{93} + 6940416 q^{94} + 5668080 q^{95} - 1769472 q^{96} + 8120252 q^{97} - 26563728 q^{98} - 10690056 q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(354))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
354.8.a \(\chi_{354}(1, \cdot)\) 354.8.a.a 1 1
354.8.a.b 5
354.8.a.c 7
354.8.a.d 8
354.8.a.e 9
354.8.a.f 9
354.8.a.g 9
354.8.a.h 10
354.8.a.i 10
354.8.c \(\chi_{354}(353, \cdot)\) n/a 140 1
354.8.e \(\chi_{354}(7, \cdot)\) n/a 1960 28
354.8.g \(\chi_{354}(11, \cdot)\) n/a 3920 28

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(354))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(354)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(118))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(177))\)\(^{\oplus 2}\)