Properties

Label 441.2.h
Level $441$
Weight $2$
Character orbit 441.h
Rep. character $\chi_{441}(214,\cdot)$
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.h (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

\( 72q + 2q^{2} + q^{3} + 66q^{4} - 5q^{5} + 2q^{6} - 12q^{8} - 7q^{9} + O(q^{10}) \) \( 72q + 2q^{2} + q^{3} + 66q^{4} - 5q^{5} + 2q^{6} - 12q^{8} - 7q^{9} + 6q^{10} + 3q^{11} + 20q^{12} + 3q^{13} + 10q^{15} + 54q^{16} - 9q^{17} - 26q^{18} - 4q^{20} + 4q^{23} - 6q^{24} - 21q^{25} - 16q^{26} + 7q^{27} - 18q^{29} - 15q^{30} - 6q^{31} - 82q^{32} - 29q^{33} - 70q^{36} + 3q^{37} - 19q^{38} + 11q^{39} + 6q^{40} - 10q^{41} - 11q^{44} + 19q^{45} - 12q^{46} + 54q^{47} + 5q^{48} - 45q^{50} + 58q^{51} + 15q^{52} + 16q^{53} - q^{54} + 6q^{55} - 15q^{57} + 9q^{58} + 60q^{59} + 5q^{60} + 12q^{62} + 12q^{64} - 60q^{65} - 34q^{66} - 12q^{67} - 30q^{68} - 6q^{69} + 6q^{71} - 36q^{72} - 12q^{73} + 41q^{74} + 26q^{75} - 6q^{76} + 69q^{78} - 36q^{79} - 19q^{80} - 55q^{81} - 18q^{83} + 3q^{85} + 25q^{86} - 5q^{87} - 9q^{88} - 41q^{89} - 25q^{90} - 52q^{92} - 50q^{93} - 6q^{94} + 34q^{95} - 59q^{96} + 3q^{97} - 34q^{99} + O(q^{100}) \)

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.h.a \(2\) \(3.521\) \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-1\) \(0\) \(q+q^{2}+(1-2\zeta_{6})q^{3}-q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
441.2.h.b \(6\) \(3.521\) 6.0.309123.1 None \(-2\) \(-2\) \(-5\) \(0\) \(q+(\beta _{2}+\beta _{3})q^{2}+(-\beta _{1}-\beta _{2}+\beta _{5})q^{3}+\cdots\)
441.2.h.c \(6\) \(3.521\) 6.0.309123.1 None \(-2\) \(2\) \(5\) \(0\) \(q+(\beta _{2}+\beta _{3})q^{2}+(\beta _{1}+\beta _{2}-\beta _{5})q^{3}+\cdots\)
441.2.h.d \(6\) \(3.521\) \(\Q(\zeta_{18})\) None \(6\) \(0\) \(-3\) \(0\) \(q+(1-\zeta_{18}^{3}-\zeta_{18}^{4})q^{2}+(\zeta_{18}^{2}+\zeta_{18}^{5})q^{3}+\cdots\)
441.2.h.e \(6\) \(3.521\) \(\Q(\zeta_{18})\) None \(6\) \(0\) \(3\) \(0\) \(q+(1-\zeta_{18}^{3}-\zeta_{18}^{4})q^{2}+(-\zeta_{18}^{2}+\cdots)q^{3}+\cdots\)
441.2.h.f \(10\) \(3.521\) 10.0.\(\cdots\).1 None \(-4\) \(1\) \(-4\) \(0\) \(q+(-\beta _{1}+\beta _{5})q^{2}+\beta _{8}q^{3}+(1-\beta _{4}+\cdots)q^{4}+\cdots\)
441.2.h.g \(12\) \(3.521\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(4\) \(0\) \(0\) \(0\) \(q+\beta _{2}q^{2}+\beta _{10}q^{3}+(1+\beta _{2}+\beta _{4})q^{4}+\cdots\)
441.2.h.h \(24\) \(3.521\) None \(-8\) \(0\) \(0\) \(0\)

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

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