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Properties

Label 304.5.w
Level $304$
Weight $5$
Character orbit 304.w
Rep. character $\chi_{304}(69,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $632$
Sturm bound $200$

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Defining parameters

Level: \( N \) \(=\) \( 304 = 2^{4} \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 304.w (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 304 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(200\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(304, [\chi])\).

Total New Old
Modular forms 648 648 0
Cusp forms 632 632 0
Eisenstein series 16 16 0

Trace form

\( 632 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + O(q^{10}) \) \( 632 q - 6 q^{2} - 6 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 900 q^{10} - 8 q^{11} - 6 q^{13} + 90 q^{14} - 12 q^{15} - 478 q^{16} - 4 q^{17} + 700 q^{19} + 2596 q^{20} + 480 q^{21} - 6 q^{22} - 3130 q^{24} - 1436 q^{26} - 2310 q^{28} - 6 q^{29} + 4240 q^{30} - 3156 q^{32} - 12 q^{33} - 5316 q^{34} + 6432 q^{35} + 1998 q^{36} + 2306 q^{38} + 264 q^{40} + 8490 q^{42} - 2 q^{43} - 14036 q^{44} - 2832 q^{45} - 4 q^{47} - 6 q^{48} - 200328 q^{49} + 12090 q^{51} - 18966 q^{52} - 6 q^{53} - 10384 q^{54} + 8980 q^{58} - 6 q^{59} - 26760 q^{60} - 7554 q^{61} - 15522 q^{62} + 9600 q^{63} - 23564 q^{64} - 12502 q^{66} - 6 q^{67} - 8344 q^{68} + 60264 q^{70} - 36594 q^{72} + 6214 q^{74} + 11462 q^{76} + 19200 q^{77} + 48690 q^{78} - 12 q^{79} - 7538 q^{80} + 207032 q^{81} - 37038 q^{82} + 23992 q^{83} - 8702 q^{85} - 6 q^{86} - 83706 q^{90} + 14400 q^{91} - 9342 q^{92} + 160 q^{93} - 25352 q^{95} + 138816 q^{96} - 12 q^{97} + 29046 q^{98} + 36092 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(304, [\chi])\) into newform subspaces

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