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Properties

Label 138.6
Level 138
Weight 6
Dimension 658
Nonzero newspaces 4
Sturm bound 6336
Trace bound 1

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Defining parameters

Level: \( N \) = \( 138 = 2 \cdot 3 \cdot 23 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(6336\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(138))\).

Total New Old
Modular forms 2728 658 2070
Cusp forms 2552 658 1894
Eisenstein series 176 0 176

Trace form

\( 658 q - 8 q^{2} + 18 q^{3} - 32 q^{4} + 132 q^{5} + 72 q^{6} - 352 q^{7} - 128 q^{8} - 162 q^{9} + O(q^{10}) \) \( 658 q - 8 q^{2} + 18 q^{3} - 32 q^{4} + 132 q^{5} + 72 q^{6} - 352 q^{7} - 128 q^{8} - 162 q^{9} + 528 q^{10} + 120 q^{11} + 288 q^{12} + 1316 q^{13} - 1408 q^{14} - 10450 q^{15} - 512 q^{16} + 16712 q^{17} + 11848 q^{18} + 1212 q^{19} - 5632 q^{20} - 21846 q^{21} - 20816 q^{22} - 41168 q^{23} + 1152 q^{24} - 5190 q^{25} + 19168 q^{26} + 45744 q^{27} + 35904 q^{28} + 33776 q^{29} + 28864 q^{30} + 7668 q^{31} - 2048 q^{32} - 83602 q^{33} + 3312 q^{34} - 8668 q^{35} - 2592 q^{36} + 161148 q^{37} - 7648 q^{38} + 49536 q^{39} + 8448 q^{40} - 37024 q^{41} + 12672 q^{42} - 145344 q^{43} + 1920 q^{44} + 10692 q^{45} - 2400 q^{46} - 106808 q^{47} + 4608 q^{48} - 68598 q^{49} - 9848 q^{50} + 63432 q^{51} + 21056 q^{52} + 206456 q^{53} + 216592 q^{54} + 297880 q^{55} - 22528 q^{56} - 139542 q^{57} - 44592 q^{58} - 369700 q^{59} - 103136 q^{60} + 62180 q^{61} + 28736 q^{62} - 42922 q^{63} - 8192 q^{64} - 86856 q^{65} + 310720 q^{66} + 33608 q^{67} + 13248 q^{68} + 506450 q^{69} + 92928 q^{70} - 12240 q^{71} + 76928 q^{72} + 51116 q^{73} + 67664 q^{74} - 738030 q^{75} - 30592 q^{76} + 21120 q^{77} - 530232 q^{78} + 165828 q^{79} + 33792 q^{80} - 195766 q^{81} - 153552 q^{82} + 230780 q^{83} + 228448 q^{84} - 25652 q^{85} - 106528 q^{86} - 140502 q^{87} + 7680 q^{88} - 236752 q^{89} + 42768 q^{90} - 497112 q^{91} - 9600 q^{92} - 64656 q^{93} + 157440 q^{94} - 1893540 q^{95} + 18432 q^{96} - 1507932 q^{97} - 102440 q^{98} + 628602 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(138))\)

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
138.6.a \(\chi_{138}(1, \cdot)\) 138.6.a.a 1 1
138.6.a.b 1
138.6.a.c 1
138.6.a.d 1
138.6.a.e 2
138.6.a.f 2
138.6.a.g 3
138.6.a.h 3
138.6.a.i 4
138.6.d \(\chi_{138}(137, \cdot)\) 138.6.d.a 40 1
138.6.e \(\chi_{138}(13, \cdot)\) n/a 200 10
138.6.f \(\chi_{138}(5, \cdot)\) n/a 400 10

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(138))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(138)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 2}\)