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Properties

Label 114.3
Level 114
Weight 3
Dimension 180
Nonzero newspaces 6
Newform subspaces 8
Sturm bound 2160
Trace bound 1

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Defining parameters

Level: \( N \) = \( 114 = 2 \cdot 3 \cdot 19 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 8 \)
Sturm bound: \(2160\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(114))\).

Total New Old
Modular forms 792 180 612
Cusp forms 648 180 468
Eisenstein series 144 0 144

Trace form

\( 180 q + O(q^{10}) \) \( 180 q + 36 q^{12} + 240 q^{13} + 144 q^{14} + 108 q^{15} + 36 q^{17} - 84 q^{19} - 72 q^{20} - 126 q^{21} - 216 q^{22} - 180 q^{23} - 504 q^{25} - 288 q^{26} + 36 q^{27} - 120 q^{28} + 288 q^{29} + 216 q^{31} + 216 q^{33} + 144 q^{35} - 108 q^{39} - 144 q^{41} - 432 q^{43} - 1026 q^{45} - 360 q^{47} - 72 q^{48} - 432 q^{49} - 576 q^{51} - 108 q^{54} + 90 q^{57} + 144 q^{60} + 168 q^{61} + 576 q^{63} + 360 q^{65} + 720 q^{66} + 576 q^{67} + 702 q^{69} + 144 q^{71} + 144 q^{72} + 108 q^{73} + 540 q^{77} + 576 q^{78} + 744 q^{79} + 936 q^{81} + 864 q^{82} + 900 q^{83} + 540 q^{84} + 1296 q^{85} + 576 q^{86} + 576 q^{87} + 36 q^{89} + 360 q^{90} - 336 q^{91} + 144 q^{92} + 36 q^{93} - 108 q^{95} - 324 q^{97} - 576 q^{98} - 1602 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(114))\)

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
114.3.c \(\chi_{114}(77, \cdot)\) 114.3.c.a 12 1
114.3.d \(\chi_{114}(37, \cdot)\) 114.3.d.a 8 1
114.3.f \(\chi_{114}(31, \cdot)\) 114.3.f.a 8 2
114.3.f.b 8
114.3.g \(\chi_{114}(11, \cdot)\) 114.3.g.a 24 2
114.3.j \(\chi_{114}(13, \cdot)\) 114.3.j.a 12 6
114.3.j.b 24
114.3.k \(\chi_{114}(5, \cdot)\) 114.3.k.a 84 6

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(114))\) into lower level spaces

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