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Properties

Label 121.2.c
Level $121$
Weight $2$
Character orbit 121.c
Rep. character $\chi_{121}(3,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $20$
Newform subspaces $5$
Sturm bound $22$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 121 = 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 121.c (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 5 \)
Sturm bound: \(22\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(121, [\chi])\).

Total New Old
Modular forms 68 52 16
Cusp forms 20 20 0
Eisenstein series 48 32 16

Trace form

\( 20 q - q^{3} - q^{5} + 4 q^{9} + O(q^{10}) \) \( 20 q - q^{3} - q^{5} + 4 q^{9} - 24 q^{12} - 4 q^{14} - 5 q^{15} + 6 q^{16} - 8 q^{20} - 28 q^{23} + 12 q^{25} + 14 q^{26} - 7 q^{27} - 5 q^{31} - 8 q^{34} + 6 q^{36} - 7 q^{37} - 12 q^{38} + 16 q^{42} + 16 q^{45} - 8 q^{47} + 19 q^{49} - 12 q^{53} + 48 q^{56} - 18 q^{58} - 11 q^{59} + 14 q^{60} + 10 q^{64} + 12 q^{67} - 19 q^{69} - 4 q^{70} - 15 q^{71} + 12 q^{75} + 80 q^{78} + 22 q^{80} + 19 q^{81} - 22 q^{82} - 24 q^{86} + 12 q^{89} + 20 q^{91} - 10 q^{92} + 17 q^{93} + 23 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(121, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
121.2.c.a 121.c 11.c $4$ $0.966$ \(\Q(\zeta_{10})\) None \(-2\) \(1\) \(-1\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-2+2\zeta_{10}-2\zeta_{10}^{2}+2\zeta_{10}^{3})q^{2}+\cdots\)
121.2.c.b 121.c 11.c $4$ $0.966$ \(\Q(\zeta_{10})\) None \(-1\) \(-2\) \(-1\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
121.2.c.c 121.c 11.c $4$ $0.966$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-11}) \) \(0\) \(1\) \(3\) \(0\) $\mathrm{U}(1)[D_{5}]$ \(q-\zeta_{10}^{2}q^{3}+2\zeta_{10}^{3}q^{4}+3\zeta_{10}q^{5}+\cdots\)
121.2.c.d 121.c 11.c $4$ $0.966$ \(\Q(\zeta_{10})\) None \(1\) \(-2\) \(-1\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+2\zeta_{10}^{2}q^{3}+\cdots\)
121.2.c.e 121.c 11.c $4$ $0.966$ \(\Q(\zeta_{10})\) None \(2\) \(1\) \(-1\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(2-2\zeta_{10}+2\zeta_{10}^{2}-2\zeta_{10}^{3})q^{2}+\cdots\)