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Properties

Label 441.3.n
Level $441$
Weight $3$
Character orbit 441.n
Rep. character $\chi_{441}(128,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $152$
Newform subspaces $9$
Sturm bound $168$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 441.n (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 9 \)
Sturm bound: \(168\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(441, [\chi])\).

Total New Old
Modular forms 240 168 72
Cusp forms 208 152 56
Eisenstein series 32 16 16

Trace form

\( 152 q + 3 q^{2} + q^{3} + 143 q^{4} + 8 q^{6} + 5 q^{9} + O(q^{10}) \) \( 152 q + 3 q^{2} + q^{3} + 143 q^{4} + 8 q^{6} + 5 q^{9} - 6 q^{10} - 19 q^{12} + 7 q^{13} - 26 q^{15} - 253 q^{16} + 27 q^{17} + 91 q^{18} + 16 q^{19} - 6 q^{20} - 12 q^{22} - 78 q^{24} - 598 q^{25} + 84 q^{26} - 65 q^{27} + 96 q^{29} - 84 q^{30} - 17 q^{31} + 135 q^{32} - 104 q^{33} + 6 q^{34} + 212 q^{36} + 13 q^{37} - 250 q^{39} - 96 q^{40} + 78 q^{41} + 28 q^{43} - 183 q^{44} - 206 q^{45} + 6 q^{46} - 105 q^{47} - 169 q^{48} - 519 q^{50} + 136 q^{51} + 34 q^{52} + 72 q^{53} + 404 q^{54} - 66 q^{55} - 195 q^{57} + 66 q^{58} - 42 q^{59} + 530 q^{60} - 56 q^{61} - 760 q^{64} + 678 q^{65} + 791 q^{66} + 34 q^{67} + 252 q^{69} + 303 q^{72} + 100 q^{73} + 323 q^{75} - 134 q^{76} + 567 q^{78} - 56 q^{79} - 3 q^{80} + 161 q^{81} + 6 q^{82} - 354 q^{83} + 81 q^{85} - 17 q^{87} - 222 q^{88} + 477 q^{89} - 247 q^{90} + 1506 q^{92} - 458 q^{93} + 183 q^{94} + 15 q^{95} - 1412 q^{96} - 17 q^{97} + 80 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(441, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
441.3.n.a 441.n 63.n $2$ $12.016$ \(\Q(\sqrt{-3}) \) None \(3\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2-\zeta_{6})q^{2}-3q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
441.3.n.b 441.n 63.n $2$ $12.016$ \(\Q(\sqrt{-3}) \) None \(3\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(2-\zeta_{6})q^{2}+3q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
441.3.n.c 441.n 63.n $6$ $12.016$ 6.0.63369648.1 None \(3\) \(9\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\beta _{5})q^{2}-3\beta _{2}q^{3}+(\beta _{1}-4\beta _{2}+\cdots)q^{4}+\cdots\)
441.3.n.d 441.n 63.n $8$ $12.016$ 8.0.3317760000.3 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{5}q^{2}+(\beta _{2}-\beta _{6}+\beta _{7})q^{3}+\beta _{4}q^{4}+\cdots\)
441.3.n.e 441.n 63.n $16$ $12.016$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{3}q^{2}+(\beta _{6}+\beta _{9})q^{3}+(2+\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
441.3.n.f 441.n 63.n $22$ $12.016$ None \(-6\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
441.3.n.g 441.n 63.n $24$ $12.016$ None \(0\) \(-10\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
441.3.n.h 441.n 63.n $24$ $12.016$ None \(0\) \(10\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
441.3.n.i 441.n 63.n $48$ $12.016$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(441, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(441, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)