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Properties

Label 378.4.ba
Level $378$
Weight $4$
Character orbit 378.ba
Rep. character $\chi_{378}(47,\cdot)$
Character field $\Q(\zeta_{18})$
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.ba (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 189 \)
Character field: \(\Q(\zeta_{18})\)
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

\( 432 q + 36 q^{6} - 192 q^{9} + O(q^{10}) \) \( 432 q + 36 q^{6} - 192 q^{9} + 48 q^{11} + 132 q^{14} - 132 q^{15} - 12 q^{21} - 60 q^{23} - 42 q^{29} + 252 q^{30} + 168 q^{36} - 564 q^{39} + 1824 q^{42} + 990 q^{45} + 594 q^{47} + 1188 q^{49} - 1464 q^{50} - 2520 q^{51} - 2520 q^{53} + 528 q^{56} + 2784 q^{57} - 1008 q^{60} + 162 q^{61} + 3270 q^{63} + 13824 q^{64} - 1128 q^{65} + 3600 q^{66} + 1728 q^{68} - 2340 q^{69} - 540 q^{70} - 720 q^{71} - 96 q^{72} - 2520 q^{74} + 3324 q^{77} + 1416 q^{78} - 2808 q^{79} + 4536 q^{81} + 408 q^{84} + 4320 q^{85} - 1200 q^{86} + 1080 q^{91} - 240 q^{92} - 3720 q^{93} + 3246 q^{95} - 324 q^{99} + O(q^{100}) \)

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

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