Properties

Label 555.2.bb
Level $555$
Weight $2$
Character orbit 555.bb
Rep. character $\chi_{555}(454,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $72$
Newform subspaces $1$
Sturm bound $152$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 555 = 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 555.bb (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 185 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(152\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(555, [\chi])\).

Total New Old
Modular forms 160 72 88
Cusp forms 144 72 72
Eisenstein series 16 0 16

Trace form

\( 72q + 32q^{4} - 2q^{5} + 36q^{9} + O(q^{10}) \) \( 72q + 32q^{4} - 2q^{5} + 36q^{9} - 8q^{11} - 16q^{14} - 24q^{16} + 4q^{19} + 4q^{20} + 12q^{21} + 10q^{25} + 24q^{26} + 16q^{29} + 12q^{30} + 24q^{31} - 44q^{34} - 2q^{35} + 64q^{36} - 8q^{39} + 46q^{40} - 48q^{41} - 8q^{44} - 4q^{45} - 64q^{46} + 32q^{49} - 46q^{50} - 8q^{51} - 12q^{55} - 72q^{56} + 32q^{59} - 68q^{60} - 8q^{61} - 136q^{64} - 42q^{65} - 32q^{66} - 4q^{69} + 4q^{70} + 12q^{71} - 96q^{74} - 8q^{75} + 8q^{76} - 8q^{79} - 44q^{80} - 36q^{81} + 136q^{84} + 4q^{85} + 8q^{86} + 8q^{91} - 28q^{94} + 18q^{95} - 20q^{96} - 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(555, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
555.2.bb.a \(72\) \(4.432\) None \(0\) \(0\) \(-2\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(555, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(555, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 2}\)