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Properties

Label 1288.2.bw
Level $1288$
Weight $2$
Character orbit 1288.bw
Rep. character $\chi_{1288}(9,\cdot)$
Character field $\Q(\zeta_{33})$
Dimension $960$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 1288 = 2^{3} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1288.bw (of order \(33\) and degree \(20\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 161 \)
Character field: \(\Q(\zeta_{33})\)
Sturm bound: \(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1288, [\chi])\).

Total New Old
Modular forms 4000 960 3040
Cusp forms 3680 960 2720
Eisenstein series 320 0 320

Trace form

\( 960 q - 4 q^{5} + 52 q^{9} + O(q^{10}) \) \( 960 q - 4 q^{5} + 52 q^{9} + 4 q^{11} + 16 q^{15} - 8 q^{17} + 16 q^{19} + 12 q^{21} - 10 q^{23} + 40 q^{25} + 24 q^{29} - 14 q^{35} + 44 q^{37} + 4 q^{39} + 16 q^{41} - 88 q^{43} + 108 q^{45} + 12 q^{47} + 46 q^{49} + 36 q^{51} + 8 q^{53} + 24 q^{55} - 120 q^{57} + 44 q^{59} - 12 q^{63} + 24 q^{65} + 8 q^{67} - 12 q^{69} + 8 q^{73} + 16 q^{75} - 12 q^{77} - 52 q^{81} - 16 q^{83} - 156 q^{85} + 138 q^{87} - 12 q^{89} - 40 q^{91} + 24 q^{93} - 116 q^{95} - 24 q^{97} - 364 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1288, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1288, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1288, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(322, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(644, [\chi])\)\(^{\oplus 2}\)