Properties

Label 588.4.t
Level $588$
Weight $4$
Character orbit 588.t
Rep. character $\chi_{588}(41,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $336$
Sturm bound $448$

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Defining parameters

Level: \( N \) \(=\) \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 588.t (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 147 \)
Character field: \(\Q(\zeta_{14})\)
Sturm bound: \(448\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(588, [\chi])\).

Total New Old
Modular forms 2052 336 1716
Cusp forms 1980 336 1644
Eisenstein series 72 0 72

Trace form

\( 336 q + 20 q^{7} - 70 q^{9} + O(q^{10}) \) \( 336 q + 20 q^{7} - 70 q^{9} + 84 q^{15} + 24 q^{21} - 1484 q^{25} + 42 q^{27} + 518 q^{37} + 560 q^{39} - 476 q^{43} + 1484 q^{45} - 1040 q^{49} - 168 q^{51} - 5334 q^{55} - 1232 q^{57} - 2366 q^{61} - 1200 q^{63} - 1708 q^{67} - 1820 q^{69} - 4620 q^{75} + 2240 q^{79} - 3374 q^{81} - 1512 q^{85} - 728 q^{87} - 6552 q^{91} + 2408 q^{93} - 8288 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(588, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(588, [\chi])\) into lower level spaces

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