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Properties

Label 147.10.m
Level $147$
Weight $10$
Character orbit 147.m
Rep. character $\chi_{147}(4,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $1008$
Sturm bound $186$

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Defining parameters

Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 147.m (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{21})\)
Sturm bound: \(186\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(147, [\chi])\).

Total New Old
Modular forms 2040 1008 1032
Cusp forms 1992 1008 984
Eisenstein series 48 0 48

Trace form

\( 1008 q + 162 q^{3} + 21504 q^{4} + 568 q^{5} - 5184 q^{6} + 188 q^{7} - 1428 q^{8} + 551124 q^{9} + O(q^{10}) \) \( 1008 q + 162 q^{3} + 21504 q^{4} + 568 q^{5} - 5184 q^{6} + 188 q^{7} - 1428 q^{8} + 551124 q^{9} + 32182 q^{10} - 3332 q^{11} + 124416 q^{12} - 498788 q^{13} + 17938 q^{14} + 96390 q^{15} + 6042232 q^{16} + 1568188 q^{17} - 6876010 q^{19} + 6159576 q^{20} - 1834164 q^{21} + 8419460 q^{22} + 1835512 q^{23} + 17756496 q^{24} + 34807822 q^{25} + 11904106 q^{26} - 2125764 q^{27} - 23871444 q^{28} + 6457192 q^{29} + 5384232 q^{30} - 55276408 q^{31} + 9452534 q^{32} + 2818638 q^{33} - 10621976 q^{34} - 5458376 q^{35} - 282175488 q^{36} + 49639380 q^{37} - 38482262 q^{38} + 23011128 q^{39} + 210430206 q^{40} + 41844568 q^{41} - 63401616 q^{42} + 43431724 q^{43} - 228406080 q^{44} - 48446424 q^{45} + 24678724 q^{46} + 119581292 q^{47} + 1003167504 q^{48} + 290192436 q^{49} - 1101374708 q^{50} - 117877032 q^{51} - 747292692 q^{52} - 467866364 q^{53} + 17006112 q^{54} - 948927142 q^{55} + 672040176 q^{56} - 197780940 q^{57} + 868404166 q^{58} + 899227036 q^{59} - 313826562 q^{60} - 16889690 q^{61} - 811763620 q^{62} + 93507372 q^{63} - 1352847440 q^{64} - 254103528 q^{65} + 175049100 q^{66} - 269584294 q^{67} - 1326403668 q^{68} - 124942824 q^{69} - 1079861884 q^{70} + 834055992 q^{71} + 37476432 q^{72} - 414440062 q^{73} + 1125092710 q^{74} + 712562022 q^{75} + 2348144982 q^{76} + 1723293164 q^{77} + 768849732 q^{78} + 11133108 q^{79} - 1718154274 q^{80} + 3615924564 q^{81} - 11641100594 q^{82} + 999940252 q^{83} + 2758233384 q^{84} - 428475264 q^{85} + 9343376532 q^{86} - 1732525200 q^{87} - 10623525024 q^{88} - 3089173936 q^{89} - 422292204 q^{90} - 4806107786 q^{91} + 4652674236 q^{92} - 31133970 q^{93} + 10447823892 q^{94} + 11303696544 q^{95} + 9250502454 q^{96} - 6753814068 q^{97} + 17218690654 q^{98} - 648121824 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(147, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{10}^{\mathrm{old}}(147, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(147, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)