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Properties

Label 712.6.j
Level $712$
Weight $6$
Character orbit 712.j
Rep. character $\chi_{712}(233,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $226$
Sturm bound $540$

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Defining parameters

Level: \( N \) \(=\) \( 712 = 2^{3} \cdot 89 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 712.j (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 89 \)
Character field: \(\Q(i)\)
Sturm bound: \(540\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(712, [\chi])\).

Total New Old
Modular forms 908 226 682
Cusp forms 892 226 666
Eisenstein series 16 0 16

Trace form

\( 226 q + 22 q^{3} + O(q^{10}) \) \( 226 q + 22 q^{3} + 1492 q^{11} + 812 q^{13} + 2868 q^{15} + 686 q^{19} - 1076 q^{23} - 149214 q^{25} - 6296 q^{27} + 16888 q^{29} - 4364 q^{31} + 12088 q^{33} - 3668 q^{35} + 33348 q^{37} + 54318 q^{41} - 29090 q^{43} + 24300 q^{45} + 37240 q^{51} + 53340 q^{57} + 17398 q^{59} + 133292 q^{61} - 8908 q^{65} - 143644 q^{67} + 164416 q^{73} + 66482 q^{75} + 6272 q^{77} - 1326830 q^{81} + 93798 q^{83} - 516376 q^{85} - 65766 q^{89} - 288208 q^{91} - 397656 q^{93} - 239720 q^{95} - 268108 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(712, [\chi])\) into newform subspaces

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

Decomposition of \(S_{6}^{\mathrm{old}}(712, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(712, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(89, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(178, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(356, [\chi])\)\(^{\oplus 2}\)