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Properties

Label 1386.4.bw
Level $1386$
Weight $4$
Character orbit 1386.bw
Rep. character $\chi_{1386}(445,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $2304$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1386.bw (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 693 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1386, [\chi])\).

Total New Old
Modular forms 6976 2304 4672
Cusp forms 6848 2304 4544
Eisenstein series 128 0 128

Trace form

\( 2304 q + 1152 q^{4} + 96 q^{9} + O(q^{10}) \) \( 2304 q + 1152 q^{4} + 96 q^{9} - 16 q^{11} - 120 q^{15} + 4608 q^{16} - 272 q^{17} + 112 q^{18} - 280 q^{21} + 336 q^{23} - 14400 q^{25} - 120 q^{26} - 36 q^{27} + 832 q^{29} - 1212 q^{33} - 780 q^{35} - 256 q^{36} - 756 q^{39} + 128 q^{41} - 1304 q^{42} + 32 q^{44} - 768 q^{45} - 224 q^{50} - 2884 q^{51} - 2212 q^{53} - 612 q^{55} + 1288 q^{57} + 1512 q^{58} - 1000 q^{59} - 640 q^{60} + 3968 q^{62} - 1292 q^{63} - 36864 q^{64} - 1280 q^{65} + 2528 q^{66} + 2176 q^{68} - 3440 q^{69} - 72 q^{70} - 512 q^{71} - 672 q^{72} + 5224 q^{75} - 676 q^{77} - 4512 q^{78} + 1620 q^{79} + 6020 q^{81} - 1992 q^{83} + 2160 q^{84} + 1440 q^{85} - 800 q^{86} + 1556 q^{87} + 2720 q^{89} - 5088 q^{90} + 1008 q^{92} - 592 q^{93} - 3232 q^{95} + 2880 q^{98} + 7252 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1386, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1386, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1386, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(693, [\chi])\)\(^{\oplus 2}\)