Properties

Label 441.3.k
Level $441$
Weight $3$
Character orbit 441.k
Rep. character $\chi_{441}(31,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $152$
Newform subspaces $3$
Sturm bound $168$
Trace bound $2$

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Defining parameters

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

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

\( 152 q - q^{2} + 3 q^{3} - 145 q^{4} - 12 q^{6} - 8 q^{8} - 11 q^{9} + O(q^{10}) \) \( 152 q - q^{2} + 3 q^{3} - 145 q^{4} - 12 q^{6} - 8 q^{8} - 11 q^{9} + 6 q^{10} + 26 q^{11} + 3 q^{12} - 15 q^{13} + 32 q^{15} - 261 q^{16} + 33 q^{17} + 23 q^{18} + 6 q^{19} - 108 q^{20} + 4 q^{22} + 116 q^{23} - 42 q^{24} - 598 q^{25} - 54 q^{26} + 81 q^{27} - 112 q^{29} + 36 q^{30} - 45 q^{31} - 135 q^{32} + 114 q^{33} - 12 q^{34} + 196 q^{36} - 9 q^{37} + 172 q^{39} + 234 q^{41} - 36 q^{43} - 195 q^{44} - 276 q^{45} - 2 q^{46} + 111 q^{47} - 147 q^{48} - 475 q^{50} - 168 q^{51} - 160 q^{53} - 378 q^{54} - 265 q^{57} + 34 q^{58} - 42 q^{59} - 450 q^{60} - 120 q^{61} + 792 q^{64} - 156 q^{65} + 447 q^{66} + 34 q^{67} - 78 q^{69} + 662 q^{71} + 455 q^{72} + 6 q^{73} + 850 q^{74} + 123 q^{75} - 72 q^{76} + 377 q^{78} + 88 q^{79} + 609 q^{80} + 177 q^{81} + 18 q^{82} - 738 q^{83} - 39 q^{85} - 170 q^{86} - 3 q^{87} + 98 q^{88} - 21 q^{89} + 543 q^{90} - 690 q^{92} - 110 q^{93} + 3 q^{94} - 525 q^{95} + 582 q^{96} + 57 q^{97} + 66 q^{99} + O(q^{100}) \)

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.k.a 441.k 63.k $28$ $12.016$ None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
441.3.k.b 441.k 63.k $28$ $12.016$ None \(1\) \(3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
441.3.k.c 441.k 63.k $96$ $12.016$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

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

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