Properties

Label 441.2.i
Level $441$
Weight $2$
Character orbit 441.i
Rep. character $\chi_{441}(68,\cdot)$
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.i (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

\( 72q + 3q^{3} - 62q^{4} + 3q^{5} - 6q^{6} + q^{9} + O(q^{10}) \) \( 72q + 3q^{3} - 62q^{4} + 3q^{5} - 6q^{6} + q^{9} + 6q^{10} + 15q^{11} + 12q^{12} + 3q^{13} - 28q^{15} + 46q^{16} - 9q^{17} - 4q^{18} + 6q^{19} - 6q^{20} - 8q^{22} + 18q^{23} + 6q^{24} - 21q^{25} + 6q^{26} + 27q^{27} + 6q^{29} - 39q^{30} + 3q^{33} - 6q^{34} - 2q^{36} + q^{37} - 27q^{38} - 29q^{39} - 24q^{40} - 6q^{41} - 8q^{43} - 69q^{44} - 39q^{45} + 16q^{46} - 30q^{47} - 15q^{48} + 3q^{50} - 18q^{51} + 15q^{52} - 36q^{53} - 27q^{54} + 35q^{57} + q^{58} + 36q^{59} + 153q^{60} + 24q^{62} - 28q^{64} + 48q^{66} - 12q^{67} + 24q^{68} - 12q^{69} - 40q^{72} + 6q^{73} + 129q^{74} + 6q^{75} - 85q^{78} + 36q^{79} - 45q^{80} - 39q^{81} - 30q^{83} - 21q^{85} - 63q^{86} + 3q^{87} + 23q^{88} + 27q^{89} + 51q^{90} - 84q^{92} + 16q^{93} - 51q^{96} + 3q^{97} - 84q^{99} + O(q^{100}) \)

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.i.a \(2\) \(3.521\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(0\) \(q+(1-2\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-q^{4}+\cdots\)
441.2.i.b \(10\) \(3.521\) 10.0.\(\cdots\).1 None \(0\) \(3\) \(0\) \(0\) \(q+(-\beta _{3}-\beta _{5})q^{2}+(-\beta _{1}+\beta _{7})q^{3}+\cdots\)
441.2.i.c \(12\) \(3.521\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{3}+\beta _{5})q^{2}+(\beta _{2}-\beta _{9})q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots\)
441.2.i.d \(48\) \(3.521\) None \(0\) \(0\) \(0\) \(0\)

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

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