Properties

Label 1386.2.m
Level $1386$
Weight $2$
Character orbit 1386.m
Rep. character $\chi_{1386}(379,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $120$
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.m (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1386, [\chi])\).

Total New Old
Modular forms 1216 120 1096
Cusp forms 1088 120 968
Eisenstein series 128 0 128

Trace form

\( 120q - 2q^{2} - 30q^{4} - 4q^{5} - 2q^{8} + O(q^{10}) \) \( 120q - 2q^{2} - 30q^{4} - 4q^{5} - 2q^{8} - 22q^{11} - 28q^{13} - 30q^{16} + 4q^{17} - 34q^{19} - 4q^{20} + 2q^{22} + 8q^{23} + 18q^{25} + 4q^{26} + 16q^{29} + 32q^{31} + 8q^{32} - 4q^{34} - 4q^{35} + 28q^{37} + 36q^{38} + 4q^{41} + 44q^{43} + 8q^{44} + 24q^{46} - 20q^{47} - 30q^{49} - 38q^{50} + 32q^{52} - 32q^{53} + 100q^{55} - 12q^{58} + 10q^{59} - 24q^{61} - 24q^{62} - 30q^{64} + 72q^{65} - 60q^{67} + 4q^{68} - 8q^{70} - 32q^{71} + 44q^{73} - 52q^{74} - 4q^{76} + 8q^{77} + 56q^{79} - 4q^{80} - 18q^{82} + 34q^{83} - 36q^{85} + 54q^{86} + 2q^{88} + 36q^{89} - 36q^{91} + 8q^{92} + 64q^{95} - 46q^{97} + 8q^{98} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1386, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(66, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(77, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(154, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(198, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(231, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(462, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(693, [\chi])\)\(^{\oplus 2}\)