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Properties

Label 378.4.v
Level $378$
Weight $4$
Character orbit 378.v
Rep. character $\chi_{378}(67,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $432$
Sturm bound $288$

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Defining parameters

Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 378.v (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 189 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(288\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(378, [\chi])\).

Total New Old
Modular forms 1320 432 888
Cusp forms 1272 432 840
Eisenstein series 48 0 48

Trace form

\( 432 q - 12 q^{6} - 192 q^{9} + O(q^{10}) \) \( 432 q - 12 q^{6} - 192 q^{9} - 48 q^{11} - 132 q^{14} + 132 q^{15} + 408 q^{17} - 12 q^{21} + 60 q^{23} + 936 q^{26} + 42 q^{29} - 252 q^{30} - 576 q^{33} - 1656 q^{35} + 168 q^{36} + 1116 q^{39} - 1236 q^{41} - 1824 q^{42} + 330 q^{45} - 198 q^{47} - 1188 q^{49} - 1464 q^{50} - 2520 q^{51} - 840 q^{53} - 360 q^{54} - 528 q^{56} + 2784 q^{57} + 3000 q^{59} - 1008 q^{60} + 54 q^{61} + 2976 q^{62} + 1938 q^{63} - 13824 q^{64} - 4968 q^{65} - 4320 q^{66} - 576 q^{68} - 1824 q^{69} - 540 q^{70} + 240 q^{71} + 96 q^{72} - 1728 q^{73} - 2520 q^{74} + 3072 q^{75} + 4308 q^{77} - 5688 q^{78} + 2808 q^{79} + 960 q^{80} + 5448 q^{81} + 408 q^{84} - 4320 q^{85} + 1200 q^{86} + 1608 q^{87} + 6408 q^{89} + 1080 q^{91} + 240 q^{92} + 3720 q^{93} - 3672 q^{94} + 5010 q^{95} - 5424 q^{98} + 2844 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(378, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(378, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(378, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)