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Properties

Label 3078.2.z
Level $3078$
Weight $2$
Character orbit 3078.z
Rep. character $\chi_{3078}(739,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $360$
Sturm bound $1080$

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Defining parameters

Level: \( N \) \(=\) \( 3078 = 2 \cdot 3^{4} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3078.z (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 513 \)
Character field: \(\Q(\zeta_{9})\)
Sturm bound: \(1080\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3078, [\chi])\).

Total New Old
Modular forms 3312 360 2952
Cusp forms 3168 360 2808
Eisenstein series 144 0 144

Trace form

\( 360 q - 12 q^{2} + 360 q^{4} - 12 q^{8} + O(q^{10}) \) \( 360 q - 12 q^{2} + 360 q^{4} - 12 q^{8} + 3 q^{11} + 360 q^{16} + 15 q^{17} - 9 q^{19} - 9 q^{22} + 24 q^{23} + 18 q^{29} - 12 q^{32} + 9 q^{34} - 18 q^{35} + 3 q^{38} - 21 q^{41} + 3 q^{44} + 114 q^{47} + 60 q^{50} - 48 q^{53} + 27 q^{59} + 36 q^{61} + 18 q^{62} + 360 q^{64} - 60 q^{65} + 36 q^{67} + 15 q^{68} - 6 q^{71} + 27 q^{73} - 9 q^{76} + 42 q^{77} - 9 q^{82} + 39 q^{83} + 60 q^{86} - 9 q^{88} + 18 q^{89} + 24 q^{92} + 72 q^{95} - 18 q^{97} + 36 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3078, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3078, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3078, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(513, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1026, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1539, [\chi])\)\(^{\oplus 2}\)