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Properties

Label 138.7
Level 138
Weight 7
Dimension 788
Nonzero newspaces 4
Sturm bound 7392
Trace bound 1

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Defining parameters

Level: \( N \) = \( 138 = 2 \cdot 3 \cdot 23 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(7392\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(138))\).

Total New Old
Modular forms 3256 788 2468
Cusp forms 3080 788 2292
Eisenstein series 176 0 176

Trace form

\( 788 q - 84 q^{3} + 128 q^{4} + 384 q^{6} - 8 q^{7} - 612 q^{9} + O(q^{10}) \) \( 788 q - 84 q^{3} + 128 q^{4} + 384 q^{6} - 8 q^{7} - 612 q^{9} - 3840 q^{10} + 2688 q^{12} + 11800 q^{13} + 9424 q^{15} - 4096 q^{16} - 45760 q^{17} + 29504 q^{18} + 42328 q^{19} + 78848 q^{20} + 81672 q^{21} - 768 q^{22} - 131648 q^{23} - 12288 q^{24} - 226084 q^{25} - 109120 q^{26} - 1428 q^{27} + 101632 q^{28} + 234080 q^{29} + 230528 q^{30} + 146008 q^{31} - 470816 q^{33} + 101376 q^{34} - 143000 q^{35} + 19584 q^{36} - 1029608 q^{37} + 311952 q^{39} + 122880 q^{40} + 470800 q^{41} + 768 q^{42} + 883624 q^{43} - 483840 q^{45} - 115968 q^{46} - 1036816 q^{47} - 86016 q^{48} - 1811964 q^{49} - 159192 q^{51} - 377600 q^{52} + 367840 q^{53} - 1089584 q^{54} + 2597040 q^{55} + 3121800 q^{57} + 49920 q^{58} - 1603448 q^{59} + 450304 q^{60} + 250264 q^{61} - 3428824 q^{63} + 131072 q^{64} - 2133056 q^{66} - 1754792 q^{67} + 1192976 q^{69} - 7680 q^{70} + 1455104 q^{72} + 2922040 q^{73} + 8014700 q^{75} + 673024 q^{76} - 3078480 q^{78} - 4554008 q^{79} - 6706716 q^{81} - 379392 q^{82} + 1237280 q^{83} + 247552 q^{84} - 208296 q^{85} + 4742040 q^{87} + 24576 q^{88} + 1967240 q^{89} - 587520 q^{90} + 23600 q^{91} - 1923432 q^{93} + 4070400 q^{94} + 9420224 q^{95} + 393216 q^{96} - 3843872 q^{97} - 8453632 q^{98} - 10390128 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(138))\)

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
138.7.b \(\chi_{138}(91, \cdot)\) 138.7.b.a 24 1
138.7.c \(\chi_{138}(47, \cdot)\) 138.7.c.a 44 1
138.7.g \(\chi_{138}(29, \cdot)\) n/a 480 10
138.7.h \(\chi_{138}(7, \cdot)\) n/a 240 10

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

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(138))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(138)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 2}\)