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Properties

Label 1008.3.bd
Level $1008$
Weight $3$
Character orbit 1008.bd
Rep. character $\chi_{1008}(65,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $188$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1008.bd (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1008, [\chi])\).

Total New Old
Modular forms 792 196 596
Cusp forms 744 188 556
Eisenstein series 48 8 40

Trace form

\( 188 q + q^{3} + q^{7} - q^{9} + O(q^{10}) \) \( 188 q + q^{3} + q^{7} - q^{9} - 2 q^{13} - 5 q^{15} + 2 q^{19} - 36 q^{21} - 862 q^{25} + 4 q^{27} + 66 q^{29} + 23 q^{31} + 35 q^{33} - 75 q^{35} - 2 q^{37} + 31 q^{39} - 6 q^{41} - 46 q^{43} + 139 q^{45} + 3 q^{47} - q^{49} - 157 q^{51} - 42 q^{55} + 30 q^{57} + 3 q^{59} + q^{61} - 135 q^{63} + 141 q^{65} - q^{67} + 149 q^{69} - 2 q^{73} - 276 q^{75} + 141 q^{77} - q^{79} - 73 q^{81} - 354 q^{83} - 27 q^{85} - 80 q^{87} - 72 q^{89} - 190 q^{91} - 143 q^{93} + 501 q^{95} - 2 q^{97} - 173 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1008, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1008, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)