Properties

Label 441.3.bj
Level $441$
Weight $3$
Character orbit 441.bj
Rep. character $\chi_{441}(10,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $552$
Newform subspaces $5$
Sturm bound $168$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 441.bj (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{42})\)
Newform subspaces: \( 5 \)
Sturm bound: \(168\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 1392 576 816
Cusp forms 1296 552 744
Eisenstein series 96 24 72

Trace form

\( 552 q + 13 q^{2} + 79 q^{4} + 8 q^{5} + 24 q^{8} + O(q^{10}) \) \( 552 q + 13 q^{2} + 79 q^{4} + 8 q^{5} + 24 q^{8} - 62 q^{10} + 49 q^{11} - 14 q^{13} + 141 q^{14} + 187 q^{16} + 13 q^{17} + 57 q^{19} - 42 q^{20} + 26 q^{22} - 75 q^{23} - 230 q^{25} + 24 q^{28} - 134 q^{29} + 45 q^{31} - 21 q^{32} - 42 q^{34} - 12 q^{35} - 171 q^{37} + 496 q^{38} + 54 q^{40} + 210 q^{41} + 42 q^{43} + 8 q^{44} + 64 q^{46} + 219 q^{47} - 144 q^{49} - 44 q^{50} + 222 q^{52} + 183 q^{53} - 245 q^{55} - 1256 q^{56} + 492 q^{58} - 14 q^{59} + 583 q^{61} - 350 q^{62} - 324 q^{64} + 20 q^{65} + 155 q^{67} + 57 q^{68} - 420 q^{70} - 35 q^{71} + 199 q^{73} - 134 q^{74} - 231 q^{76} - 39 q^{77} + 75 q^{79} + 1140 q^{80} + 1622 q^{82} + 462 q^{83} + 262 q^{85} + 1517 q^{86} + 2003 q^{88} - 270 q^{89} - 244 q^{91} + 818 q^{92} - 76 q^{94} + 217 q^{95} - 1261 q^{98} + O(q^{100}) \)

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.bj.a 441.bj 49.h $12$ $12.016$ \(\Q(\zeta_{21})\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-13\) $\mathrm{U}(1)[D_{42}]$ \(q+(4\zeta_{21}^{3}+4\zeta_{21}^{10})q^{4}+(-5+5\zeta_{21}+\cdots)q^{7}+\cdots\)
441.3.bj.b 441.bj 49.h $96$ $12.016$ None \(13\) \(0\) \(14\) \(-14\) $\mathrm{SU}(2)[C_{42}]$
441.3.bj.c 441.bj 49.h $108$ $12.016$ None \(0\) \(0\) \(-9\) \(7\) $\mathrm{SU}(2)[C_{42}]$
441.3.bj.d 441.bj 49.h $120$ $12.016$ None \(0\) \(0\) \(3\) \(-6\) $\mathrm{SU}(2)[C_{42}]$
441.3.bj.e 441.bj 49.h $216$ $12.016$ None \(0\) \(0\) \(0\) \(26\) $\mathrm{SU}(2)[C_{42}]$

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

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