↑

Properties

Label 1386.2.ch
Level $1386$
Weight $2$
Character orbit 1386.ch
Rep. character $\chi_{1386}(149,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $768$
Sturm bound $576$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.ch (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 693 \)
Character field: \(\Q(\zeta_{30})\)
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

\( 768 q - 192 q^{4} + 12 q^{9} + O(q^{10}) \) \( 768 q - 192 q^{4} + 12 q^{9} + 12 q^{11} + 12 q^{15} - 192 q^{16} + 36 q^{23} - 96 q^{25} + 36 q^{26} + 18 q^{27} - 84 q^{33} - 150 q^{35} - 8 q^{36} + 20 q^{39} + 40 q^{42} + 12 q^{44} - 64 q^{45} - 40 q^{51} + 36 q^{53} - 12 q^{55} + 40 q^{57} - 18 q^{58} - 8 q^{60} + 110 q^{63} - 192 q^{64} + 48 q^{66} - 136 q^{69} + 12 q^{70} + 40 q^{72} - 28 q^{75} - 54 q^{77} - 80 q^{78} - 92 q^{81} + 20 q^{84} + 24 q^{86} - 60 q^{89} + 80 q^{90} - 54 q^{92} + 14 q^{93} - 94 q^{99} + O(q^{100}) \)

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

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