Properties

Label 441.2.g
Level $441$
Weight $2$
Character orbit 441.g
Rep. character $\chi_{441}(67,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $72$
Newform subspaces $8$
Sturm bound $112$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.g (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 8 \)
Sturm bound: \(112\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(441, [\chi])\).

Total New Old
Modular forms 128 88 40
Cusp forms 96 72 24
Eisenstein series 32 16 16

Trace form

\( 72q - q^{2} + q^{3} - 33q^{4} + 10q^{5} + 2q^{6} - 12q^{8} - q^{9} + O(q^{10}) \) \( 72q - q^{2} + q^{3} - 33q^{4} + 10q^{5} + 2q^{6} - 12q^{8} - q^{9} + 6q^{10} - 6q^{11} - 19q^{12} + 3q^{13} + 10q^{15} - 27q^{16} - 9q^{17} + 19q^{18} - 4q^{20} - 8q^{23} - 12q^{24} + 42q^{25} - 16q^{26} + 7q^{27} - 18q^{29} + 72q^{30} + 3q^{31} + 41q^{32} + 16q^{33} - 70q^{36} + 3q^{37} + 38q^{38} - 28q^{39} - 12q^{40} - 10q^{41} - 11q^{44} + 4q^{45} - 12q^{46} - 27q^{47} + 5q^{48} - 45q^{50} - 14q^{51} - 30q^{52} + 16q^{53} + 62q^{54} + 6q^{55} - 15q^{57} - 18q^{58} - 30q^{59} - 16q^{60} + 12q^{62} + 12q^{64} + 30q^{65} + 41q^{66} + 6q^{67} + 60q^{68} - 6q^{69} + 6q^{71} - 51q^{72} - 12q^{73} - 82q^{74} - 43q^{75} - 6q^{76} + 69q^{78} + 18q^{79} - 19q^{80} - q^{81} - 18q^{83} + 3q^{85} - 50q^{86} - 29q^{87} + 18q^{88} - 41q^{89} - 25q^{90} - 52q^{92} + 58q^{93} + 3q^{94} - 17q^{95} - 14q^{96} + 3q^{97} - 34q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(441, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
441.2.g.a \(2\) \(3.521\) \(\Q(\sqrt{-3}) \) None \(-1\) \(3\) \(2\) \(0\) \(q+(-1+\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
441.2.g.b \(6\) \(3.521\) \(\Q(\zeta_{18})\) None \(-3\) \(0\) \(-6\) \(0\) \(q+(-1+\zeta_{18}+\zeta_{18}^{5})q^{2}+(\zeta_{18}^{2}+\zeta_{18}^{4}+\cdots)q^{3}+\cdots\)
441.2.g.c \(6\) \(3.521\) \(\Q(\zeta_{18})\) None \(-3\) \(0\) \(6\) \(0\) \(q+(-1+\zeta_{18}+\zeta_{18}^{5})q^{2}+(-\zeta_{18}^{2}+\cdots)q^{3}+\cdots\)
441.2.g.d \(6\) \(3.521\) 6.0.309123.1 None \(1\) \(-2\) \(10\) \(0\) \(q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{2}+(-1+\cdots)q^{3}+\cdots\)
441.2.g.e \(6\) \(3.521\) 6.0.309123.1 None \(1\) \(2\) \(-10\) \(0\) \(q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{2}+(1-\beta _{1}+\cdots)q^{3}+\cdots\)
441.2.g.f \(10\) \(3.521\) 10.0.\(\cdots\).1 None \(2\) \(-2\) \(8\) \(0\) \(q+\beta _{1}q^{2}+(-\beta _{2}+\beta _{7})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)
441.2.g.g \(12\) \(3.521\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-2\) \(0\) \(0\) \(0\) \(q+(-\beta _{2}+\beta _{5})q^{2}+(-\beta _{8}-\beta _{10})q^{3}+\cdots\)
441.2.g.h \(24\) \(3.521\) None \(4\) \(0\) \(0\) \(0\)

Decomposition of \(S_{2}^{\mathrm{old}}(441, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(441, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)