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Properties

Label 3024.2.fj
Level $3024$
Weight $2$
Character orbit 3024.fj
Rep. character $\chi_{3024}(209,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $852$
Sturm bound $1152$

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Defining parameters

Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3024.fj (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 189 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(1152\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3024, [\chi])\).

Total New Old
Modular forms 3528 876 2652
Cusp forms 3384 852 2532
Eisenstein series 144 24 120

Trace form

\( 852 q + 6 q^{7} - 12 q^{9} + O(q^{10}) \) \( 852 q + 6 q^{7} - 12 q^{9} + 12 q^{11} + 12 q^{15} - 6 q^{21} + 12 q^{23} - 12 q^{25} + 12 q^{29} + 9 q^{35} - 6 q^{37} + 48 q^{39} + 12 q^{43} - 6 q^{49} - 6 q^{51} - 30 q^{57} + 36 q^{63} - 36 q^{65} + 12 q^{67} + 18 q^{71} + 18 q^{77} + 12 q^{79} + 12 q^{81} + 18 q^{85} + 3 q^{91} - 12 q^{93} + 258 q^{95} - 204 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3024, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3024, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3024, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1512, [\chi])\)\(^{\oplus 2}\)