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Properties

Label 1386.4.bu
Level $1386$
Weight $4$
Character orbit 1386.bu
Rep. character $\chi_{1386}(701,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $288$
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.bu (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 33 \)
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 288 3232
Cusp forms 3392 288 3104
Eisenstein series 128 0 128

Trace form

\( 288 q - 288 q^{4} + O(q^{10}) \) \( 288 q - 288 q^{4} - 1152 q^{16} - 144 q^{22} + 3168 q^{25} - 2304 q^{31} + 576 q^{34} - 1008 q^{37} - 1440 q^{46} + 3528 q^{49} + 3840 q^{52} + 7344 q^{55} + 1728 q^{58} - 3600 q^{61} - 4608 q^{64} - 1248 q^{67} + 2016 q^{70} - 720 q^{73} + 9360 q^{79} - 576 q^{82} + 3240 q^{85} - 576 q^{88} - 9216 q^{97} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1386, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(198, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(462, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(693, [\chi])\)\(^{\oplus 2}\)