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Properties

Label 1386.2.bw
Level $1386$
Weight $2$
Character orbit 1386.bw
Rep. character $\chi_{1386}(445,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $768$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.bw (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 693 \)
Character field: \(\Q(\zeta_{15})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1386, [\chi])\).

Total New Old
Modular forms 2368 768 1600
Cusp forms 2240 768 1472
Eisenstein series 128 0 128

Trace form

\( 768 q + 96 q^{4} - 12 q^{9} + O(q^{10}) \) \( 768 q + 96 q^{4} - 12 q^{9} + 8 q^{11} - 12 q^{15} + 96 q^{16} + 16 q^{17} - 8 q^{18} + 20 q^{21} - 24 q^{23} - 192 q^{25} - 12 q^{26} + 18 q^{27} + 16 q^{29} + 48 q^{33} + 30 q^{35} + 8 q^{36} - 48 q^{39} + 68 q^{41} + 4 q^{42} - 4 q^{44} + 72 q^{45} + 16 q^{50} - 40 q^{51} - 52 q^{53} + 12 q^{55} + 4 q^{57} - 36 q^{58} + 20 q^{59} - 16 q^{60} - 64 q^{62} - 122 q^{63} - 192 q^{64} - 8 q^{65} + 32 q^{66} - 32 q^{68} + 136 q^{69} + 12 q^{70} + 64 q^{71} + 12 q^{72} - 116 q^{75} + 74 q^{77} + 48 q^{78} - 36 q^{79} - 112 q^{81} + 24 q^{83} - 36 q^{84} - 24 q^{85} + 16 q^{86} + 164 q^{87} + 20 q^{89} - 48 q^{90} - 18 q^{92} - 100 q^{93} - 16 q^{95} - 98 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1386, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1386, [\chi])\) into lower level spaces

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