Properties

Label 1386.2.ce
Level $1386$
Weight $2$
Character orbit 1386.ce
Rep. character $\chi_{1386}(19,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $320$
Sturm bound $576$

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.ce (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
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 2432 320 2112
Cusp forms 2176 320 1856
Eisenstein series 256 0 256

Trace form

\( 320q - 40q^{4} + 12q^{5} - 10q^{7} + O(q^{10}) \) \( 320q - 40q^{4} + 12q^{5} - 10q^{7} - 2q^{14} + 40q^{16} - 30q^{17} - 16q^{22} + 8q^{23} - 36q^{25} + 48q^{26} - 10q^{28} + 20q^{29} + 18q^{31} - 70q^{35} + 8q^{37} - 12q^{38} + 30q^{40} - 10q^{44} - 24q^{47} + 18q^{49} - 8q^{53} + 4q^{56} - 8q^{58} + 60q^{59} + 30q^{61} + 80q^{64} + 32q^{67} + 30q^{68} + 34q^{70} + 56q^{71} + 90q^{73} + 20q^{74} + 34q^{77} + 30q^{79} + 18q^{80} + 12q^{82} + 140q^{85} + 26q^{86} + 2q^{88} + 84q^{89} - 22q^{91} - 44q^{92} + 90q^{95} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1386, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(462, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(693, [\chi])\)\(^{\oplus 2}\)