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Properties

Label 441.3.v
Level $441$
Weight $3$
Character orbit 441.v
Rep. character $\chi_{441}(55,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $270$
Newform subspaces $3$
Sturm bound $168$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 441.v (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{14})\)
Newform subspaces: \( 3 \)
Sturm bound: \(168\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 696 282 414
Cusp forms 648 270 378
Eisenstein series 48 12 36

Trace form

\( 270 q + 5 q^{2} - 89 q^{4} + 7 q^{5} - 16 q^{7} - 9 q^{8} + O(q^{10}) \) \( 270 q + 5 q^{2} - 89 q^{4} + 7 q^{5} - 16 q^{7} - 9 q^{8} - 7 q^{10} - 28 q^{11} - 7 q^{13} - 75 q^{14} - 117 q^{16} + 56 q^{17} + 63 q^{20} - 41 q^{22} + 18 q^{23} + 186 q^{25} - 105 q^{26} - 218 q^{28} + 149 q^{29} + 165 q^{32} + 21 q^{34} + 243 q^{35} + 260 q^{37} + 119 q^{38} - 735 q^{40} + 105 q^{41} + 13 q^{43} + 319 q^{44} - 79 q^{46} - 378 q^{47} - 32 q^{49} + 80 q^{50} - 119 q^{52} - 390 q^{53} + 77 q^{55} + 308 q^{56} + 501 q^{58} - 343 q^{59} - 147 q^{61} - 217 q^{62} - 619 q^{64} + 19 q^{65} + 156 q^{67} + 891 q^{70} + 50 q^{71} - 70 q^{73} + 359 q^{74} + 210 q^{76} + 174 q^{77} + 332 q^{79} - 392 q^{82} + 735 q^{83} - 277 q^{85} + 157 q^{86} + 397 q^{88} + 903 q^{89} + 565 q^{91} - 908 q^{92} + 826 q^{94} - 298 q^{95} + 571 q^{98} + O(q^{100}) \)

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.v.a 441.v 49.f $54$ $12.016$ None \(5\) \(0\) \(7\) \(0\) $\mathrm{SU}(2)[C_{14}]$
441.3.v.b 441.v 49.f $108$ $12.016$ None \(0\) \(0\) \(0\) \(-14\) $\mathrm{SU}(2)[C_{14}]$
441.3.v.c 441.v 49.f $108$ $12.016$ None \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{14}]$

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

\( S_{3}^{\mathrm{old}}(441, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 2}\)