↑

Properties

Label 693.6.ch
Level $693$
Weight $6$
Character orbit 693.ch
Rep. character $\chi_{693}(13,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $3808$
Sturm bound $576$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 693.ch (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 693 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(693, [\chi])\).

Total New Old
Modular forms 3872 3872 0
Cusp forms 3808 3808 0
Eisenstein series 64 64 0

Trace form

\( 3808 q - 10 q^{2} - 7558 q^{4} - 5 q^{7} - 40 q^{8} + 648 q^{9} + O(q^{10}) \) \( 3808 q - 10 q^{2} - 7558 q^{4} - 5 q^{7} - 40 q^{8} + 648 q^{9} + 182 q^{11} + 125 q^{14} + 2610 q^{15} + 118650 q^{16} - 20 q^{18} + 120 q^{22} - 148 q^{23} - 287506 q^{25} - 20 q^{28} - 10 q^{29} - 4880 q^{30} - 18070 q^{35} + 29500 q^{36} - 24 q^{37} - 7620 q^{39} - 92445 q^{42} - 16156 q^{44} + 600 q^{46} - 3 q^{49} - 31260 q^{50} - 123820 q^{51} + 249544 q^{53} + 227358 q^{56} - 287940 q^{57} - 29846 q^{58} - 21570 q^{60} - 120335 q^{63} + 3661416 q^{64} - 16 q^{67} + 15340 q^{70} - 284440 q^{71} + 238060 q^{72} + 1664590 q^{74} - 146151 q^{77} - 602056 q^{78} - 10 q^{79} - 398848 q^{81} - 387725 q^{84} - 10 q^{85} + 4378 q^{86} - 69704 q^{88} - 67240 q^{91} - 60738 q^{92} - 328434 q^{93} - 261650 q^{95} + 1034140 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(693, [\chi])\) into newform subspaces

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