Properties

Label 684.3.bl
Level $684$
Weight $3$
Character orbit 684.bl
Rep. character $\chi_{684}(373,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $80$
Newform subspaces $1$
Sturm bound $360$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 684.bl (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 171 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(360\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(684, [\chi])\).

Total New Old
Modular forms 492 80 412
Cusp forms 468 80 388
Eisenstein series 24 0 24

Trace form

\( 80q - 6q^{3} - q^{7} - 2q^{9} + O(q^{10}) \) \( 80q - 6q^{3} - q^{7} - 2q^{9} - 6q^{11} - 15q^{13} + 24q^{15} - 21q^{17} - 20q^{19} + 24q^{23} + 400q^{25} + 63q^{27} + 24q^{31} + 30q^{33} - 54q^{35} - 81q^{39} + 76q^{43} + 188q^{45} + 24q^{47} - 267q^{49} - 243q^{51} - 36q^{53} + 72q^{57} + 14q^{61} + 284q^{63} + 288q^{65} - 21q^{67} - 48q^{69} - 81q^{71} + 55q^{73} - 165q^{75} + 30q^{77} - 51q^{79} - 110q^{81} - 93q^{83} + 306q^{87} + 216q^{89} + 96q^{91} + 204q^{93} - 432q^{95} + 90q^{97} + 260q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(684, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
684.3.bl.a \(80\) \(18.638\) None \(0\) \(-6\) \(0\) \(-1\)

Decomposition of \(S_{3}^{\mathrm{old}}(684, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(684, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 2}\)