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

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

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

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