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Properties

Label 309.5.l
Level $309$
Weight $5$
Character orbit 309.l
Rep. character $\chi_{309}(8,\cdot)$
Character field $\Q(\zeta_{34})$
Dimension $2176$
Sturm bound $173$

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Defining parameters

Level: \( N \) \(=\) \( 309 = 3 \cdot 103 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 309.l (of order \(34\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 309 \)
Character field: \(\Q(\zeta_{34})\)
Sturm bound: \(173\)

Dimensions

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

Total New Old
Modular forms 2240 2240 0
Cusp forms 2176 2176 0
Eisenstein series 64 64 0

Trace form

\( 2176 q - 25 q^{3} + 1026 q^{4} + 17 q^{6} - 34 q^{7} - 185 q^{9} + O(q^{10}) \) \( 2176 q - 25 q^{3} + 1026 q^{4} + 17 q^{6} - 34 q^{7} - 185 q^{9} - 1170 q^{10} + 205 q^{12} - 354 q^{13} - 259 q^{15} - 8310 q^{16} + 13 q^{18} + 78 q^{19} + 6535 q^{21} + 142 q^{22} - 305 q^{24} + 6822 q^{25} - 655 q^{27} + 14112 q^{28} + 2187 q^{30} + 766 q^{31} - 1387 q^{33} - 12064 q^{34} - 16843 q^{36} - 16380 q^{37} + 28015 q^{39} - 1930 q^{40} + 4213 q^{42} + 286 q^{43} + 5429 q^{45} - 1104 q^{46} - 48865 q^{48} - 39442 q^{49} + 1291 q^{51} - 3762 q^{52} + 13953 q^{54} - 17480 q^{55} - 5704 q^{57} + 28722 q^{58} + 104726 q^{60} - 1746 q^{61} + 21911 q^{63} + 108676 q^{64} - 33911 q^{66} + 19724 q^{67} + 56005 q^{69} + 754 q^{70} + 6783 q^{72} - 40310 q^{73} + 122491 q^{75} - 31806 q^{76} - 4981 q^{78} + 32522 q^{79} - 4513 q^{81} - 79098 q^{82} - 24133 q^{84} - 106388 q^{85} + 25253 q^{87} + 84506 q^{88} - 16747 q^{90} + 259026 q^{91} - 97233 q^{93} + 73718 q^{94} - 4045 q^{96} + 174698 q^{97} - 13409 q^{99} + O(q^{100}) \)

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.