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Properties

Label 1336.2.i
Level $1336$
Weight $2$
Character orbit 1336.i
Rep. character $\chi_{1336}(9,\cdot)$
Character field $\Q(\zeta_{83})$
Dimension $3444$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 1336 = 2^{3} \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1336.i (of order \(83\) and degree \(82\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 167 \)
Character field: \(\Q(\zeta_{83})\)
Sturm bound: \(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1336, [\chi])\).

Total New Old
Modular forms 14104 3444 10660
Cusp forms 13448 3444 10004
Eisenstein series 656 0 656

Trace form

\( 3444 q + 2 q^{5} - 38 q^{9} + O(q^{10}) \) \( 3444 q + 2 q^{5} - 38 q^{9} + 4 q^{11} + 2 q^{13} + 8 q^{17} + 4 q^{19} - 42 q^{25} + 12 q^{27} - 8 q^{29} + 8 q^{31} + 8 q^{33} + 12 q^{35} + 2 q^{37} - 16 q^{39} + 4 q^{41} + 2 q^{43} + 10 q^{45} - 4 q^{47} - 38 q^{49} - 24 q^{51} + 6 q^{53} - 8 q^{55} + 28 q^{57} - 18 q^{59} - 36 q^{63} - 12 q^{65} - 30 q^{67} - 12 q^{69} - 20 q^{71} + 24 q^{73} - 4 q^{75} - 8 q^{77} + 12 q^{79} - 34 q^{81} + 6 q^{83} + 16 q^{85} - 32 q^{87} - 4 q^{89} + 20 q^{91} - 24 q^{93} - 24 q^{95} - 20 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1336, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1336, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1336, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(167, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(334, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(668, [\chi])\)\(^{\oplus 2}\)