Properties

Label 684.3.be
Level $684$
Weight $3$
Character orbit 684.be
Rep. character $\chi_{684}(425,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $80$
Newform subspaces $1$
Sturm bound $360$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 684.be (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

\( 80 q + 4 q^{3} + q^{7} + 4 q^{9} + O(q^{10}) \) \( 80 q + 4 q^{3} + q^{7} + 4 q^{9} + 18 q^{11} + 10 q^{13} - 11 q^{15} + 9 q^{17} + 20 q^{19} - 30 q^{21} + 200 q^{25} + 25 q^{27} - 27 q^{29} - 8 q^{31} + 23 q^{33} + 22 q^{37} + 39 q^{39} - 54 q^{41} + 88 q^{43} - 196 q^{45} + 198 q^{47} - 267 q^{49} - 56 q^{51} + 36 q^{53} + 78 q^{57} + 171 q^{59} + 7 q^{61} + 82 q^{63} - 144 q^{65} + 154 q^{67} + 44 q^{69} + 135 q^{71} + 43 q^{73} + 69 q^{75} + 216 q^{77} + 34 q^{79} - 44 q^{81} - 171 q^{83} - 244 q^{87} - 216 q^{89} + 122 q^{91} - 104 q^{93} - 216 q^{95} + 16 q^{97} - 305 q^{99} + O(q^{100}) \)

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.be.a \(80\) \(18.638\) None \(0\) \(4\) \(0\) \(1\)

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

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