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Properties

Label 309.5.b
Level $309$
Weight $5$
Character orbit 309.b
Rep. character $\chi_{309}(104,\cdot)$
Character field $\Q$
Dimension $136$
Sturm bound $173$

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Defining parameters

Level: \( N \) \(=\) \( 309 = 3 \cdot 103 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 309.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Sturm bound: \(173\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(309, [\chi])\).

Total New Old
Modular forms 140 136 4
Cusp forms 136 136 0
Eisenstein series 4 0 4

Trace form

\( 136 q + 8 q^{3} - 1060 q^{4} - 34 q^{6} + 168 q^{9} + O(q^{10}) \) \( 136 q + 8 q^{3} - 1060 q^{4} - 34 q^{6} + 168 q^{9} - 156 q^{10} - 222 q^{12} + 320 q^{13} + 242 q^{15} + 8276 q^{16} - 30 q^{18} - 112 q^{19} - 568 q^{21} - 176 q^{22} + 288 q^{24} - 16104 q^{25} + 638 q^{27} + 1664 q^{28} - 2204 q^{30} - 800 q^{31} + 1370 q^{33} - 1536 q^{34} - 1670 q^{36} - 1504 q^{37} + 5696 q^{39} + 1896 q^{40} - 4230 q^{42} - 320 q^{43} - 5446 q^{45} + 1036 q^{46} + 17568 q^{48} + 39408 q^{49} - 1308 q^{51} + 3728 q^{52} - 13970 q^{54} + 5104 q^{55} + 5670 q^{57} - 13524 q^{58} + 5094 q^{60} + 1712 q^{61} - 21928 q^{63} - 54344 q^{64} - 922 q^{66} + 26652 q^{67} + 10346 q^{69} - 788 q^{70} - 6800 q^{72} - 31124 q^{73} + 5060 q^{75} + 31772 q^{76} + 4964 q^{78} - 32556 q^{79} + 4496 q^{81} - 65436 q^{82} + 24116 q^{84} + 37572 q^{85} - 25270 q^{87} + 7940 q^{88} + 16730 q^{90} + 5052 q^{91} - 10360 q^{93} - 5752 q^{94} + 4028 q^{96} + 9888 q^{97} + 13392 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(309, [\chi])\) into newform subspaces

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