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Properties

Label 588.3.v
Level $588$
Weight $3$
Character orbit 588.v
Rep. character $\chi_{588}(13,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $108$
Sturm bound $336$

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Defining parameters

Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 588.v (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(336\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(588, [\chi])\).

Total New Old
Modular forms 1380 108 1272
Cusp forms 1308 108 1200
Eisenstein series 72 0 72

Trace form

\( 108 q + 14 q^{7} + 54 q^{9} + O(q^{10}) \) \( 108 q + 14 q^{7} + 54 q^{9} + 34 q^{11} - 60 q^{15} - 98 q^{17} - 32 q^{23} + 98 q^{25} - 56 q^{29} + 280 q^{35} - 108 q^{37} - 180 q^{39} - 196 q^{41} + 104 q^{43} - 42 q^{45} + 266 q^{47} - 70 q^{49} + 60 q^{51} + 84 q^{53} - 308 q^{55} - 24 q^{57} - 84 q^{59} + 280 q^{61} + 42 q^{63} + 116 q^{65} - 36 q^{67} - 92 q^{71} + 126 q^{73} + 42 q^{77} + 104 q^{79} - 162 q^{81} + 994 q^{83} + 448 q^{85} + 252 q^{87} + 154 q^{89} + 280 q^{91} - 120 q^{93} + 4 q^{95} + 108 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(588, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(588, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(588, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 2}\)