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Properties

Label 1344.2.y
Level $1344$
Weight $2$
Character orbit 1344.y
Rep. character $\chi_{1344}(209,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $120$
Sturm bound $512$

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Defining parameters

Level: \( N \) \(=\) \( 1344 = 2^{6} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1344.y (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 336 \)
Character field: \(\Q(i)\)
Sturm bound: \(512\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1344, [\chi])\).

Total New Old
Modular forms 544 136 408
Cusp forms 480 120 360
Eisenstein series 64 16 48

Trace form

\( 120 q + O(q^{10}) \) \( 120 q + 8 q^{15} - 8 q^{21} - 8 q^{37} + 8 q^{43} - 8 q^{49} + 56 q^{51} - 24 q^{63} - 24 q^{67} + 16 q^{79} - 8 q^{81} - 48 q^{85} + 8 q^{91} + 8 q^{93} + 40 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1344, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1344, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1344, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 2}\)