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Properties

Label 1386.4.bs
Level $1386$
Weight $4$
Character orbit 1386.bs
Rep. character $\chi_{1386}(811,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $480$
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.bs (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 77 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1152\)

Dimensions

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

Total New Old
Modular forms 3520 480 3040
Cusp forms 3392 480 2912
Eisenstein series 128 0 128

Trace form

\( 480 q + 480 q^{4} + 20 q^{7} + O(q^{10}) \) \( 480 q + 480 q^{4} + 20 q^{7} - 20 q^{11} + 52 q^{14} - 1920 q^{16} + 296 q^{22} - 280 q^{23} + 2828 q^{25} - 120 q^{28} - 700 q^{29} - 1590 q^{35} - 624 q^{37} - 1040 q^{44} - 30 q^{49} + 1232 q^{53} - 128 q^{56} + 1344 q^{58} + 7680 q^{64} - 4512 q^{67} - 1248 q^{70} - 1688 q^{71} - 2800 q^{74} + 730 q^{77} - 4200 q^{79} - 3460 q^{85} + 904 q^{86} - 64 q^{88} + 1362 q^{91} - 2240 q^{92} + 12200 q^{95} + O(q^{100}) \)

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

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