Properties

Label 1386.2.bz
Level $1386$
Weight $2$
Character orbit 1386.bz
Rep. character $\chi_{1386}(25,\cdot)$
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.bz (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

\( 768q - 192q^{4} - 12q^{9} + O(q^{10}) \) \( 768q - 192q^{4} - 12q^{9} - 4q^{11} - 12q^{15} - 192q^{16} + 16q^{17} + 16q^{18} + 20q^{21} + 12q^{23} + 96q^{25} - 12q^{26} + 18q^{27} + 16q^{29} - 60q^{33} + 30q^{35} + 8q^{36} - 24q^{39} + 68q^{41} + 40q^{42} - 4q^{44} - 96q^{45} + 16q^{50} + 20q^{51} - 52q^{53} + 12q^{55} + 4q^{57} + 18q^{58} - 40q^{59} + 8q^{60} - 64q^{62} + 70q^{63} - 192q^{64} + 16q^{65} - 64q^{66} + 16q^{68} + 136q^{69} + 12q^{70} + 64q^{71} - 24q^{72} + 28q^{75} - 130q^{77} + 48q^{78} + 72q^{79} + 20q^{81} + 24q^{83} - 24q^{85} - 8q^{86} + 152q^{87} + 20q^{89} - 48q^{90} - 18q^{92} + 50q^{93} + 32q^{95} - 98q^{99} + O(q^{100}) \)

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

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