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Properties

Label 330.2.s
Level $330$
Weight $2$
Character orbit 330.s
Rep. character $\chi_{330}(49,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $48$
Newform subspaces $3$
Sturm bound $144$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 330 = 2 \cdot 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 330.s (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 3 \)
Sturm bound: \(144\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(330, [\chi])\).

Total New Old
Modular forms 320 48 272
Cusp forms 256 48 208
Eisenstein series 64 0 64

Trace form

\( 48q + 12q^{4} + 8q^{5} - 4q^{6} + 12q^{9} + O(q^{10}) \) \( 48q + 12q^{4} + 8q^{5} - 4q^{6} + 12q^{9} + 4q^{10} - 4q^{11} + 12q^{14} - 14q^{15} - 12q^{16} + 16q^{19} - 8q^{20} + 32q^{21} + 4q^{24} + 4q^{25} + 8q^{26} + 8q^{30} + 20q^{31} - 8q^{34} + 44q^{35} - 12q^{36} - 8q^{39} + 6q^{40} - 60q^{41} - 36q^{44} - 8q^{45} - 36q^{46} - 8q^{49} - 24q^{50} - 32q^{51} - 16q^{54} - 12q^{55} + 8q^{56} - 80q^{59} - 16q^{60} - 56q^{61} + 12q^{64} - 64q^{65} - 16q^{66} - 40q^{69} - 30q^{70} + 64q^{71} - 8q^{74} + 24q^{75} + 24q^{76} + 4q^{79} - 12q^{80} - 12q^{81} + 8q^{84} + 88q^{86} - 24q^{89} - 4q^{90} + 68q^{91} + 20q^{94} - 60q^{95} - 4q^{96} + 4q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(330, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
330.2.s.a \(8\) \(2.635\) \(\Q(\zeta_{20})\) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{20}q^{2}-\zeta_{20}^{3}q^{3}+\zeta_{20}^{2}q^{4}+(\zeta_{20}+\cdots)q^{5}+\cdots\)
330.2.s.b \(8\) \(2.635\) \(\Q(\zeta_{20})\) None \(0\) \(0\) \(10\) \(0\) \(q+\zeta_{20}q^{2}-\zeta_{20}^{3}q^{3}+\zeta_{20}^{2}q^{4}+(2\zeta_{20}^{2}+\cdots)q^{5}+\cdots\)
330.2.s.c \(32\) \(2.635\) None \(0\) \(0\) \(-2\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(330, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(330, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(165, [\chi])\)\(^{\oplus 2}\)