Properties

Label 378.4.z
Level $378$
Weight $4$
Character orbit 378.z
Rep. character $\chi_{378}(41,\cdot)$
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.z (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

\( 432 q + 96 q^{9} + O(q^{10}) \) \( 432 q + 96 q^{9} - 24 q^{11} + 132 q^{14} - 132 q^{15} + 204 q^{21} + 1164 q^{23} + 84 q^{29} + 1008 q^{30} + 2484 q^{35} - 336 q^{36} - 564 q^{39} - 912 q^{42} - 594 q^{49} - 456 q^{50} - 2520 q^{51} + 528 q^{56} - 3264 q^{57} + 2016 q^{60} + 1272 q^{63} + 13824 q^{64} + 1212 q^{65} + 1080 q^{70} - 720 q^{71} + 192 q^{72} - 2520 q^{74} - 11292 q^{77} + 1416 q^{78} + 5616 q^{79} - 2268 q^{81} - 816 q^{84} + 4320 q^{85} + 2400 q^{86} - 540 q^{91} - 3264 q^{92} - 9192 q^{93} + 600 q^{95} + 8136 q^{98} - 18216 q^{99} + O(q^{100}) \)

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

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