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Properties

Label 3078.2.dy
Level $3078$
Weight $2$
Character orbit 3078.dy
Rep. character $\chi_{3078}(167,\cdot)$
Character field $\Q(\zeta_{54})$
Dimension $3240$
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.dy (of order \(54\) and degree \(18\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1539 \)
Character field: \(\Q(\zeta_{54})\)
Sturm bound: \(1080\)

Dimensions

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

Total New Old
Modular forms 9792 3240 6552
Cusp forms 9648 3240 6408
Eisenstein series 144 0 144

Trace form

\( 3240 q + O(q^{10}) \) \( 3240 q + 9 q^{11} + 18 q^{12} + 54 q^{22} + 36 q^{23} - 54 q^{29} + 27 q^{33} + 108 q^{35} + 63 q^{38} - 9 q^{41} - 72 q^{42} + 18 q^{45} + 36 q^{50} - 63 q^{51} - 54 q^{54} - 9 q^{57} + 117 q^{59} - 72 q^{65} - 27 q^{67} - 63 q^{68} - 90 q^{69} + 144 q^{71} - 72 q^{77} + 36 q^{83} + 36 q^{87} + 72 q^{90} - 36 q^{92} - 54 q^{95} + O(q^{100}) \)

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

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