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Properties

Label 114.8
Level 114
Weight 8
Dimension 628
Nonzero newspaces 6
Sturm bound 5760
Trace bound 1

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Defining parameters

Level: \( N \) = \( 114 = 2 \cdot 3 \cdot 19 \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(5760\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(114))\).

Total New Old
Modular forms 2592 628 1964
Cusp forms 2448 628 1820
Eisenstein series 144 0 144

Trace form

\( 628 q - 16 q^{2} - 54 q^{3} - 128 q^{4} + 228 q^{5} - 432 q^{6} + 3152 q^{7} - 1024 q^{8} - 1458 q^{9} + O(q^{10}) \) \( 628 q - 16 q^{2} - 54 q^{3} - 128 q^{4} + 228 q^{5} - 432 q^{6} + 3152 q^{7} - 1024 q^{8} - 1458 q^{9} + 1824 q^{10} - 14664 q^{11} + 6912 q^{12} + 96260 q^{13} - 55712 q^{14} - 117288 q^{15} - 8192 q^{16} + 130680 q^{17} - 11664 q^{18} + 377248 q^{19} + 12288 q^{20} - 199530 q^{21} - 751920 q^{22} - 476484 q^{23} - 27648 q^{24} + 1163530 q^{25} + 1080640 q^{26} - 530721 q^{27} - 379648 q^{28} + 1279176 q^{29} + 49248 q^{30} - 914500 q^{31} - 65536 q^{32} - 2040930 q^{33} + 105696 q^{34} + 807864 q^{35} - 93312 q^{36} + 1896440 q^{37} - 198880 q^{38} + 1602342 q^{39} + 116736 q^{40} - 308400 q^{41} + 680832 q^{42} - 6015472 q^{43} - 938496 q^{44} - 9049320 q^{45} - 663168 q^{46} + 5490780 q^{47} + 258048 q^{48} + 1630290 q^{49} + 1042064 q^{50} + 4657905 q^{51} + 486656 q^{52} - 1572156 q^{53} - 5268672 q^{54} + 1671696 q^{55} + 1613824 q^{56} - 15609690 q^{57} + 665760 q^{58} - 1490280 q^{59} + 2442240 q^{60} + 3782384 q^{61} - 530432 q^{62} + 24526386 q^{63} - 524288 q^{64} - 1240356 q^{65} - 1287936 q^{66} - 15954112 q^{67} + 845568 q^{68} - 30728106 q^{69} - 2874624 q^{70} - 12844980 q^{71} + 6216192 q^{72} + 9092642 q^{73} + 583456 q^{74} + 21235716 q^{75} - 1591040 q^{76} - 30385680 q^{77} - 1548864 q^{78} + 40146596 q^{79} + 933888 q^{80} + 43503894 q^{81} + 28773024 q^{82} - 40869768 q^{83} - 18361728 q^{84} - 93700872 q^{85} - 48248192 q^{86} - 84402360 q^{87} - 7507968 q^{88} - 1419516 q^{89} + 6955056 q^{90} + 88969120 q^{91} + 36659712 q^{92} + 99385182 q^{93} + 126544512 q^{94} + 89633532 q^{95} - 1769472 q^{96} + 55979696 q^{97} - 6324240 q^{98} - 99003141 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(114))\)

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
114.8.a \(\chi_{114}(1, \cdot)\) 114.8.a.a 1 1
114.8.a.b 1
114.8.a.c 1
114.8.a.d 1
114.8.a.e 1
114.8.a.f 3
114.8.a.g 3
114.8.a.h 3
114.8.a.i 3
114.8.a.j 3
114.8.b \(\chi_{114}(113, \cdot)\) 114.8.b.a 24 1
114.8.b.b 24
114.8.e \(\chi_{114}(7, \cdot)\) 114.8.e.a 10 2
114.8.e.b 10
114.8.e.c 12
114.8.e.d 12
114.8.h \(\chi_{114}(65, \cdot)\) 114.8.h.a 48 2
114.8.h.b 48
114.8.i \(\chi_{114}(25, \cdot)\) n/a 144 6
114.8.l \(\chi_{114}(29, \cdot)\) n/a 276 6

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(114))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(114)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 1}\)