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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
121.2.c.a \(4\) \(0.966\) \(\Q(\zeta_{10})\) None \(-2\) \(1\) \(-1\) \(-2\) \(q+(-2+2\zeta_{10}-2\zeta_{10}^{2}+2\zeta_{10}^{3})q^{2}+\cdots\)
121.2.c.b \(4\) \(0.966\) \(\Q(\zeta_{10})\) None \(-1\) \(-2\) \(-1\) \(2\) \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
121.2.c.c \(4\) \(0.966\) \(\Q(\zeta_{10})\) \(\Q(\sqrt{-11}) \) \(0\) \(1\) \(3\) \(0\) \(q-\zeta_{10}^{2}q^{3}+2\zeta_{10}^{3}q^{4}+3\zeta_{10}q^{5}+\cdots\)
121.2.c.d \(4\) \(0.966\) \(\Q(\zeta_{10})\) None \(1\) \(-2\) \(-1\) \(-2\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+2\zeta_{10}^{2}q^{3}+\cdots\)
121.2.c.e \(4\) \(0.966\) \(\Q(\zeta_{10})\) None \(2\) \(1\) \(-1\) \(2\) \(q+(2-2\zeta_{10}+2\zeta_{10}^{2}-2\zeta_{10}^{3})q^{2}+\cdots\)