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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

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

Display 100 coefficients 10 coefficients

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.s.a 441.s 63.s $2$ $3.521$ \(\Q(\sqrt{-3}) \) None \(-3\) \(3\) \(6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
441.2.s.b 441.s 63.s $10$ $3.521$ 10.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{4}+\beta _{7}+\beta _{8})q^{2}+(\beta _{1}-\beta _{2}+\beta _{4}+\cdots)q^{3}+\cdots\)
441.2.s.c 441.s 63.s $12$ $3.521$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(6\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}-\beta _{10}q^{3}+(\beta _{1}+\beta _{4}+\beta _{7}+\cdots)q^{4}+\cdots\)
441.2.s.d 441.s 63.s $48$ $3.521$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

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

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