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Properties

Label 114.6
Level 114
Weight 6
Dimension 448
Nonzero newspaces 6
Sturm bound 4320
Trace bound 1

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Defining parameters

Level: \( N \) = \( 114 = 2 \cdot 3 \cdot 19 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(4320\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(114))\).

Total New Old
Modular forms 1872 448 1424
Cusp forms 1728 448 1280
Eisenstein series 144 0 144

Trace form

\( 448 q - 8 q^{2} + 18 q^{3} - 32 q^{4} + 132 q^{5} + 72 q^{6} - 352 q^{7} - 128 q^{8} - 162 q^{9} + O(q^{10}) \) \( 448 q - 8 q^{2} + 18 q^{3} - 32 q^{4} + 132 q^{5} + 72 q^{6} - 352 q^{7} - 128 q^{8} - 162 q^{9} + 528 q^{10} + 120 q^{11} - 576 q^{12} + 10004 q^{13} + 6512 q^{14} + 2376 q^{15} - 512 q^{16} - 7776 q^{17} - 648 q^{18} - 26576 q^{19} - 4224 q^{20} + 5058 q^{21} + 17544 q^{22} + 19356 q^{23} + 1152 q^{24} + 44266 q^{25} + 13184 q^{26} - 26577 q^{27} - 34240 q^{28} + 11568 q^{29} - 4752 q^{30} + 46460 q^{31} - 2048 q^{32} + 11826 q^{33} + 3312 q^{34} - 35880 q^{35} - 2592 q^{36} - 32368 q^{37} - 3824 q^{38} - 69570 q^{39} + 8448 q^{40} - 37272 q^{41} + 12672 q^{42} + 81296 q^{43} + 1920 q^{44} + 164592 q^{45} - 4800 q^{46} + 107436 q^{47} - 20736 q^{48} - 99222 q^{49} - 9848 q^{50} - 160623 q^{51} + 21056 q^{52} + 62532 q^{53} + 129168 q^{54} - 7920 q^{55} - 22528 q^{56} + 285714 q^{57} - 44592 q^{58} - 52680 q^{59} + 16128 q^{60} - 13048 q^{61} + 28736 q^{62} - 221598 q^{63} - 8192 q^{64} + 103044 q^{65} - 396288 q^{66} + 341696 q^{67} + 13248 q^{68} - 78894 q^{69} + 92928 q^{70} - 80244 q^{71} + 128448 q^{72} - 190210 q^{73} + 67664 q^{74} - 214092 q^{75} - 15296 q^{76} - 976512 q^{77} - 469152 q^{78} - 630988 q^{79} + 33792 q^{80} + 414918 q^{81} + 419856 q^{82} + 1119864 q^{83} + 490464 q^{84} + 934488 q^{85} + 254912 q^{86} + 840312 q^{87} + 7680 q^{88} + 79236 q^{89} - 320472 q^{90} - 807296 q^{91} - 550272 q^{92} - 1409454 q^{93} - 1114944 q^{94} - 880932 q^{95} + 18432 q^{96} - 1074232 q^{97} - 855816 q^{98} - 1052109 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(114))\)

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
114.6.a \(\chi_{114}(1, \cdot)\) 114.6.a.a 1 1
114.6.a.b 1
114.6.a.c 1
114.6.a.d 1
114.6.a.e 2
114.6.a.f 2
114.6.a.g 2
114.6.a.h 3
114.6.a.i 3
114.6.b \(\chi_{114}(113, \cdot)\) 114.6.b.a 16 1
114.6.b.b 16
114.6.e \(\chi_{114}(7, \cdot)\) 114.6.e.a 8 2
114.6.e.b 8
114.6.e.c 10
114.6.e.d 10
114.6.h \(\chi_{114}(65, \cdot)\) 114.6.h.a 32 2
114.6.h.b 32
114.6.i \(\chi_{114}(25, \cdot)\) 114.6.i.a 24 6
114.6.i.b 24
114.6.i.c 24
114.6.i.d 24
114.6.l \(\chi_{114}(29, \cdot)\) n/a 204 6

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(114))\) into lower level spaces

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