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Properties

Label 441.2.u
Level $441$
Weight $2$
Character orbit 441.u
Rep. character $\chi_{441}(64,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $138$
Newform subspaces $5$
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.u (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{7})\)
Newform subspaces: \( 5 \)
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 360 150 210
Cusp forms 312 138 174
Eisenstein series 48 12 36

Trace form

\( 138 q + 5 q^{2} - 29 q^{4} + 5 q^{5} - 8 q^{7} + 7 q^{8} + O(q^{10}) \) \( 138 q + 5 q^{2} - 29 q^{4} + 5 q^{5} - 8 q^{7} + 7 q^{8} + 3 q^{10} + 4 q^{11} - 9 q^{13} + 43 q^{14} - 19 q^{16} - 6 q^{17} - 38 q^{19} - 19 q^{20} + q^{22} + 28 q^{23} - 38 q^{25} - 5 q^{26} + 32 q^{28} + 43 q^{29} - 48 q^{31} - 37 q^{32} + 3 q^{34} - 5 q^{35} + 18 q^{37} + 3 q^{38} + 85 q^{40} - 5 q^{41} + 5 q^{43} - 71 q^{44} - 37 q^{46} + 14 q^{47} + 18 q^{49} - 112 q^{50} + 29 q^{52} + 24 q^{53} - 31 q^{55} + 32 q^{56} - 3 q^{58} - 9 q^{59} + 29 q^{61} + 7 q^{62} - 93 q^{64} + 11 q^{65} - 12 q^{67} + 104 q^{68} + 91 q^{70} - 26 q^{71} - 50 q^{73} - 19 q^{74} - 44 q^{76} - 18 q^{77} - 28 q^{79} + 72 q^{80} - 6 q^{82} - 5 q^{83} + 59 q^{85} - 81 q^{86} - 115 q^{88} - 21 q^{89} + 29 q^{91} + 82 q^{92} - 24 q^{94} - 28 q^{95} - 172 q^{97} - 85 q^{98} + O(q^{100}) \)

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.u.a 441.u 49.e $6$ $3.521$ \(\Q(\zeta_{14})\) None \(3\) \(0\) \(-6\) \(7\) $\mathrm{SU}(2)[C_{7}]$ \(q+(1-\zeta_{14}+\zeta_{14}^{4}-\zeta_{14}^{5})q^{2}+(-1+\cdots)q^{4}+\cdots\)
441.2.u.b 441.u 49.e $12$ $3.521$ \(\Q(\zeta_{21})\) None \(2\) \(0\) \(7\) \(-7\) $\mathrm{SU}(2)[C_{7}]$ \(q+(-\zeta_{21}^{2}-\zeta_{21}^{4}+\zeta_{21}^{5}+\zeta_{21}^{9}+\cdots)q^{2}+\cdots\)
441.2.u.c 441.u 49.e $24$ $3.521$ None \(-1\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{7}]$
441.2.u.d 441.u 49.e $36$ $3.521$ None \(1\) \(0\) \(4\) \(-6\) $\mathrm{SU}(2)[C_{7}]$
441.2.u.e 441.u 49.e $60$ $3.521$ None \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{7}]$

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

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