↑

Properties

Label 3344.2.db
Level $3344$
Weight $2$
Character orbit 3344.db
Rep. character $\chi_{3344}(241,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $708$
Sturm bound $960$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 3344 = 2^{4} \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3344.db (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 209 \)
Character field: \(\Q(\zeta_{18})\)
Sturm bound: \(960\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3344, [\chi])\).

Total New Old
Modular forms 2952 732 2220
Cusp forms 2808 708 2100
Eisenstein series 144 24 120

Trace form

\( 708 q + 12 q^{3} - 12 q^{5} - 24 q^{9} + O(q^{10}) \) \( 708 q + 12 q^{3} - 12 q^{5} - 24 q^{9} + 3 q^{11} + 12 q^{15} + 12 q^{23} - 12 q^{25} + 18 q^{27} + 18 q^{31} - 3 q^{33} - 6 q^{45} + 12 q^{47} + 312 q^{49} + 12 q^{53} + 27 q^{55} + 12 q^{59} - 132 q^{67} - 18 q^{69} + 12 q^{71} - 54 q^{77} - 90 q^{81} + 48 q^{89} + 54 q^{91} - 30 q^{93} - 60 q^{97} - 21 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3344, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(3344, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3344, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(209, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(418, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(836, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1672, [\chi])\)\(^{\oplus 2}\)