Properties

Label 3344.2.ca
Level $3344$
Weight $2$
Character orbit 3344.ca
Rep. character $\chi_{3344}(721,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $472$
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.ca (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 209 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(960\)

Dimensions

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

Total New Old
Modular forms 1968 488 1480
Cusp forms 1872 472 1400
Eisenstein series 96 16 80

Trace form

\( 472 q - 6 q^{5} + 10 q^{7} + 100 q^{9} + O(q^{10}) \) \( 472 q - 6 q^{5} + 10 q^{7} + 100 q^{9} + 8 q^{11} - 10 q^{17} + 5 q^{19} + 28 q^{23} - 116 q^{25} + 40 q^{35} + 10 q^{39} - 8 q^{45} + 6 q^{47} + 124 q^{49} - 2 q^{55} - 15 q^{57} - 10 q^{61} + 40 q^{63} - 10 q^{73} + 10 q^{77} - 148 q^{81} - 90 q^{83} + 70 q^{85} - 66 q^{93} - 45 q^{95} + 12 q^{99} + O(q^{100}) \)

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

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