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Properties

Label 114.5
Level 114
Weight 5
Dimension 356
Nonzero newspaces 6
Newform subspaces 8
Sturm bound 3600
Trace bound 3

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Defining parameters

Level: \( N \) = \( 114 = 2 \cdot 3 \cdot 19 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 8 \)
Sturm bound: \(3600\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(114))\).

Total New Old
Modular forms 1512 356 1156
Cusp forms 1368 356 1012
Eisenstein series 144 0 144

Trace form

\( 356 q + 12 q^{3} + 32 q^{4} - 96 q^{6} - 104 q^{7} + 252 q^{9} + O(q^{10}) \) \( 356 q + 12 q^{3} + 32 q^{4} - 96 q^{6} - 104 q^{7} + 252 q^{9} + 192 q^{10} + 336 q^{12} - 440 q^{13} - 1728 q^{14} - 2844 q^{15} - 256 q^{16} - 1188 q^{17} + 576 q^{18} + 3824 q^{19} + 2592 q^{20} + 4470 q^{21} + 4704 q^{22} + 3780 q^{23} + 768 q^{24} - 844 q^{25} - 3456 q^{26} + 198 q^{27} - 4448 q^{28} + 1728 q^{29} - 576 q^{30} - 2648 q^{31} - 6768 q^{33} + 2304 q^{34} - 9504 q^{35} - 2016 q^{36} - 7496 q^{37} + 8592 q^{39} - 1536 q^{40} + 9504 q^{41} - 2496 q^{42} + 22648 q^{43} - 3726 q^{45} + 4224 q^{46} - 2160 q^{47} + 3072 q^{48} - 12972 q^{49} + 15894 q^{51} + 1600 q^{52} + 15552 q^{54} - 8064 q^{55} - 12318 q^{57} - 16320 q^{58} - 10368 q^{60} + 18376 q^{61} - 30960 q^{63} + 2048 q^{64} - 10800 q^{65} - 19008 q^{66} - 22376 q^{67} + 9090 q^{69} + 4992 q^{70} - 18144 q^{71} + 11520 q^{72} - 16496 q^{73} + 4044 q^{75} - 5728 q^{76} + 93420 q^{77} + 52800 q^{78} + 80800 q^{79} + 1044 q^{81} + 9984 q^{82} - 24084 q^{83} - 39216 q^{84} - 101520 q^{85} - 62208 q^{86} - 64080 q^{87} + 10752 q^{88} - 91692 q^{89} - 71136 q^{90} - 136768 q^{91} - 25920 q^{92} - 50448 q^{93} - 19200 q^{94} + 20412 q^{95} - 6144 q^{96} + 61852 q^{97} + 103680 q^{98} + 102132 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(114))\)

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
114.5.c \(\chi_{114}(77, \cdot)\) 114.5.c.a 24 1
114.5.d \(\chi_{114}(37, \cdot)\) 114.5.d.a 12 1
114.5.f \(\chi_{114}(31, \cdot)\) 114.5.f.a 12 2
114.5.f.b 12
114.5.g \(\chi_{114}(11, \cdot)\) 114.5.g.a 56 2
114.5.j \(\chi_{114}(13, \cdot)\) 114.5.j.a 36 6
114.5.j.b 48
114.5.k \(\chi_{114}(5, \cdot)\) 114.5.k.a 156 6

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(114))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(114)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 2}\)