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Properties

Label 138.5
Level 138
Weight 5
Dimension 524
Nonzero newspaces 4
Newform subspaces 4
Sturm bound 5280
Trace bound 1

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Defining parameters

Level: \( N \) = \( 138 = 2 \cdot 3 \cdot 23 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 4 \)
Sturm bound: \(5280\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(138))\).

Total New Old
Modular forms 2200 524 1676
Cusp forms 2024 524 1500
Eisenstein series 176 0 176

Trace form

\( 524 q + 12 q^{3} + 32 q^{4} - 96 q^{6} - 104 q^{7} + 252 q^{9} + O(q^{10}) \) \( 524 q + 12 q^{3} + 32 q^{4} - 96 q^{6} - 104 q^{7} + 252 q^{9} + 192 q^{10} - 96 q^{12} - 200 q^{13} + 2350 q^{15} - 256 q^{16} - 1980 q^{17} - 2944 q^{18} - 2396 q^{19} - 3168 q^{20} - 2394 q^{21} - 1344 q^{22} + 3960 q^{23} + 768 q^{24} + 9476 q^{25} + 6336 q^{26} + 7086 q^{27} + 6112 q^{28} + 2772 q^{29} - 1984 q^{30} - 4556 q^{31} - 9278 q^{33} + 2304 q^{34} + 13200 q^{35} - 2016 q^{36} - 14536 q^{37} - 10488 q^{39} - 1536 q^{40} - 11616 q^{41} - 2496 q^{42} - 13384 q^{43} + 3456 q^{45} + 2112 q^{46} + 15840 q^{47} + 768 q^{48} + 50196 q^{49} + 10512 q^{51} + 1600 q^{52} + 14784 q^{53} - 22784 q^{54} + 736 q^{55} - 25218 q^{57} - 16320 q^{58} - 48048 q^{59} + 14464 q^{60} + 5944 q^{61} + 62102 q^{63} + 2048 q^{64} + 26560 q^{66} + 17944 q^{67} - 21406 q^{69} + 4992 q^{70} - 27136 q^{72} - 1160 q^{73} - 67522 q^{75} - 11456 q^{76} - 41760 q^{78} - 46664 q^{79} - 24780 q^{81} + 27264 q^{82} - 35904 q^{83} + 28480 q^{84} - 21552 q^{85} + 7248 q^{87} + 10752 q^{88} - 15312 q^{89} - 12096 q^{90} - 5200 q^{91} - 8904 q^{93} - 19200 q^{94} + 204204 q^{95} - 6144 q^{96} + 256804 q^{97} + 84480 q^{98} + 64380 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(138))\)

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
138.5.b \(\chi_{138}(91, \cdot)\) 138.5.b.a 16 1
138.5.c \(\chi_{138}(47, \cdot)\) 138.5.c.a 28 1
138.5.g \(\chi_{138}(29, \cdot)\) 138.5.g.a 320 10
138.5.h \(\chi_{138}(7, \cdot)\) 138.5.h.a 160 10

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(138))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(138)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 2}\)