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Properties

Label 147.7
Level 147
Weight 7
Dimension 3337
Nonzero newspaces 8
Sturm bound 10976
Trace bound 1

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Defining parameters

Level: \( N \) = \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(10976\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(147))\).

Total New Old
Modular forms 4824 3435 1389
Cusp forms 4584 3337 1247
Eisenstein series 240 98 142

Trace form

\( 3337 q - 42 q^{3} + 34 q^{4} + 672 q^{5} - 9 q^{6} - 996 q^{7} - 2820 q^{8} - 2982 q^{9} + O(q^{10}) \) \( 3337 q - 42 q^{3} + 34 q^{4} + 672 q^{5} - 9 q^{6} - 996 q^{7} - 2820 q^{8} - 2982 q^{9} + 10302 q^{10} + 16464 q^{11} + 9423 q^{12} - 9592 q^{13} - 12792 q^{14} - 9675 q^{15} - 36014 q^{16} - 3360 q^{17} - 3165 q^{18} + 81116 q^{19} - 15222 q^{21} - 132534 q^{22} + 71232 q^{23} + 186759 q^{24} + 266587 q^{25} + 13356 q^{26} - 197100 q^{27} - 162900 q^{28} - 169440 q^{29} - 105909 q^{30} - 127372 q^{31} + 221844 q^{32} + 343209 q^{33} + 400662 q^{34} + 164640 q^{35} - 42291 q^{36} - 490084 q^{37} - 123228 q^{38} - 283143 q^{39} + 1601910 q^{40} + 348096 q^{41} + 272211 q^{42} + 679556 q^{43} - 1925616 q^{44} - 227991 q^{45} - 3272754 q^{46} - 1673280 q^{47} - 750294 q^{48} + 1114884 q^{49} + 2279604 q^{50} + 1748025 q^{51} + 7854950 q^{52} + 2219280 q^{53} + 1312563 q^{54} + 2024046 q^{55} - 1788210 q^{56} - 2498169 q^{57} - 11204970 q^{58} - 6465312 q^{59} - 7786221 q^{60} - 2874340 q^{61} + 1575840 q^{62} + 700314 q^{63} + 8936230 q^{64} + 3279024 q^{65} + 4994331 q^{66} + 7759052 q^{67} + 4875192 q^{68} + 2735367 q^{69} - 604782 q^{70} - 2323488 q^{71} + 1674639 q^{72} - 3188332 q^{73} - 2529828 q^{74} - 4915896 q^{75} - 11570050 q^{76} - 2274624 q^{77} - 6475767 q^{78} + 488852 q^{79} - 19441758 q^{80} - 7674198 q^{81} + 16940280 q^{82} + 14086128 q^{83} + 21174030 q^{84} + 10194282 q^{85} + 10786482 q^{86} + 6254787 q^{87} + 5194824 q^{88} - 1302336 q^{89} - 303690 q^{90} - 9456222 q^{91} - 6449142 q^{92} - 13018221 q^{93} - 31257480 q^{94} - 26630016 q^{95} - 36393798 q^{96} - 17497930 q^{97} + 7976994 q^{98} - 3925920 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(147))\)

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
147.7.b \(\chi_{147}(50, \cdot)\) 147.7.b.a 1 1
147.7.b.b 12
147.7.b.c 12
147.7.b.d 14
147.7.b.e 14
147.7.b.f 24
147.7.d \(\chi_{147}(97, \cdot)\) 147.7.d.a 8 1
147.7.d.b 8
147.7.d.c 24
147.7.f \(\chi_{147}(19, \cdot)\) 147.7.f.a 8 2
147.7.f.b 8
147.7.f.c 8
147.7.f.d 8
147.7.f.e 24
147.7.f.f 24
147.7.h \(\chi_{147}(116, \cdot)\) n/a 152 2
147.7.j \(\chi_{147}(13, \cdot)\) n/a 336 6
147.7.l \(\chi_{147}(8, \cdot)\) n/a 660 6
147.7.n \(\chi_{147}(2, \cdot)\) n/a 1320 12
147.7.p \(\chi_{147}(10, \cdot)\) n/a 672 12

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

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(147))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(147)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)