Properties

Label 441.2.s
Level $441$
Weight $2$
Character orbit 441.s
Rep. character $\chi_{441}(362,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $72$
Newform subspaces $4$
Sturm bound $112$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(112\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

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

\( 72q + 3q^{2} + 3q^{3} + 31q^{4} + 6q^{5} + 6q^{6} - 5q^{9} + O(q^{10}) \) \( 72q + 3q^{2} + 3q^{3} + 31q^{4} + 6q^{5} + 6q^{6} - 5q^{9} + 6q^{10} + 3q^{12} - 3q^{13} - 28q^{15} - 23q^{16} + 9q^{17} + 23q^{18} + 6q^{19} + 6q^{20} - 8q^{22} - 24q^{24} + 42q^{25} - 6q^{26} - 27q^{27} + 6q^{29} + 12q^{30} + 15q^{31} - 69q^{32} + 6q^{33} + 6q^{34} - 2q^{36} + q^{37} - 54q^{38} - 26q^{39} + 6q^{41} - 8q^{43} + 69q^{44} - 6q^{45} + 16q^{46} - 15q^{47} + 15q^{48} + 3q^{50} + 42q^{51} + 36q^{53} - 36q^{54} + 35q^{57} - 2q^{58} + 18q^{59} - 96q^{60} - 36q^{61} - 24q^{62} - 28q^{64} - 36q^{65} + 33q^{66} + 6q^{67} + 48q^{68} + 12q^{69} + 5q^{72} + 6q^{73} + 33q^{75} - 85q^{78} - 18q^{79} + 45q^{80} + 87q^{81} + 30q^{83} - 21q^{85} - 39q^{87} - 46q^{88} - 27q^{89} - 51q^{90} - 84q^{92} - 26q^{93} + 3q^{94} - 141q^{95} - 12q^{96} - 3q^{97} - 84q^{99} + O(q^{100}) \)

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.s.a \(2\) \(3.521\) \(\Q(\sqrt{-3}) \) None \(-3\) \(3\) \(6\) \(0\) \(q+(-1-\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
441.2.s.b \(10\) \(3.521\) 10.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{4}+\beta _{7}+\beta _{8})q^{2}+(\beta _{1}-\beta _{2}+\beta _{4}+\cdots)q^{3}+\cdots\)
441.2.s.c \(12\) \(3.521\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(6\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{2}-\beta _{10}q^{3}+(\beta _{1}+\beta _{4}+\beta _{7}+\cdots)q^{4}+\cdots\)
441.2.s.d \(48\) \(3.521\) None \(0\) \(0\) \(0\) \(0\)

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

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