Properties

Label 441.2.f
Level $441$
Weight $2$
Character orbit 441.f
Rep. character $\chi_{441}(148,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $72$
Newform subspaces $8$
Sturm bound $112$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.f (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 8 \)
Sturm bound: \(112\)
Trace bound: \(3\)
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 92 36
Cusp forms 96 72 24
Eisenstein series 32 20 12

Trace form

\( 72q + 2q^{2} + 4q^{3} - 30q^{4} - 2q^{5} + 8q^{6} - 24q^{8} + 8q^{9} + O(q^{10}) \) \( 72q + 2q^{2} + 4q^{3} - 30q^{4} - 2q^{5} + 8q^{6} - 24q^{8} + 8q^{9} + 6q^{11} - 16q^{12} - 8q^{15} - 18q^{16} + 12q^{17} - 14q^{18} + 12q^{19} - 22q^{20} - 12q^{22} + 16q^{23} + 12q^{24} - 18q^{25} + 8q^{26} - 20q^{27} - 42q^{30} - 6q^{31} + 26q^{32} - 8q^{33} + 6q^{34} + 8q^{36} + 12q^{37} + 14q^{38} + 26q^{39} + 12q^{40} - 22q^{41} - 12q^{43} - 44q^{44} - 14q^{45} - 6q^{47} + 14q^{48} - 18q^{50} - 68q^{51} - 18q^{52} + 16q^{53} + 44q^{54} + 12q^{55} - 18q^{57} - 18q^{58} - 12q^{59} + 62q^{60} + 96q^{62} - 24q^{64} + 24q^{65} - 34q^{66} - 12q^{67} + 12q^{68} + 48q^{69} - 60q^{71} + 126q^{72} + 36q^{73} - 22q^{74} - 22q^{75} - 6q^{76} - 30q^{78} + 8q^{80} - 16q^{81} - 30q^{83} + 18q^{85} + 58q^{86} - 8q^{87} - 6q^{88} - 20q^{89} - 100q^{90} - 4q^{92} + 4q^{93} + 6q^{94} - 26q^{95} - 32q^{96} + 44q^{99} + O(q^{100}) \)

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.f.a \(2\) \(3.521\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-3\) \(-1\) \(0\) \(q+(-1+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
441.2.f.b \(2\) \(3.521\) \(\Q(\sqrt{-3}) \) None \(-1\) \(3\) \(1\) \(0\) \(q+(-1+\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
441.2.f.c \(6\) \(3.521\) \(\Q(\zeta_{18})\) None \(-3\) \(0\) \(3\) \(0\) \(q+(-1+\zeta_{18}+\zeta_{18}^{5})q^{2}+(\zeta_{18}^{3}-\zeta_{18}^{5})q^{3}+\cdots\)
441.2.f.d \(6\) \(3.521\) 6.0.309123.1 None \(1\) \(4\) \(-5\) \(0\) \(q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{2}+(-\beta _{2}+\cdots)q^{3}+\cdots\)
441.2.f.e \(10\) \(3.521\) 10.0.\(\cdots\).1 None \(2\) \(-1\) \(4\) \(0\) \(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(-1-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
441.2.f.f \(10\) \(3.521\) 10.0.\(\cdots\).1 None \(2\) \(1\) \(-4\) \(0\) \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-1-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
441.2.f.g \(12\) \(3.521\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-2\) \(0\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{6})q^{2}+\beta _{10}q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)
441.2.f.h \(24\) \(3.521\) None \(4\) \(0\) \(0\) \(0\)

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

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