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

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

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
441.2.i.a 441.i 63.i $2$ $3.521$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-2\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-q^{4}+\cdots\)
441.2.i.b 441.i 63.i $10$ $3.521$ 10.0.\(\cdots\).1 None \(0\) \(3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{3}-\beta _{5})q^{2}+(-\beta _{1}+\beta _{7})q^{3}+\cdots\)
441.2.i.c 441.i 63.i $12$ $3.521$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{3}+\beta _{5})q^{2}+(\beta _{2}-\beta _{9})q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots\)
441.2.i.d 441.i 63.i $48$ $3.521$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

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

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