Properties

Label 242.2.c
Level $242$
Weight $2$
Character orbit 242.c
Rep. character $\chi_{242}(3,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $36$
Newform subspaces $7$
Sturm bound $66$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 242 = 2 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 242.c (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 7 \)
Sturm bound: \(66\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(242, [\chi])\).

Total New Old
Modular forms 180 36 144
Cusp forms 84 36 48
Eisenstein series 96 0 96

Trace form

\( 36q + q^{2} + 6q^{3} - 9q^{4} + 8q^{5} - q^{6} - 2q^{7} + q^{8} - 15q^{9} + O(q^{10}) \) \( 36q + q^{2} + 6q^{3} - 9q^{4} + 8q^{5} - q^{6} - 2q^{7} + q^{8} - 15q^{9} - 4q^{10} - 14q^{12} + 4q^{13} - 2q^{14} - 2q^{15} - 9q^{16} - 2q^{17} + 8q^{18} + 5q^{19} + 8q^{20} + 12q^{21} - 12q^{23} - q^{24} - 13q^{25} - 4q^{26} + 3q^{27} - 2q^{28} - 10q^{29} - 6q^{30} + 10q^{31} - 4q^{32} - 18q^{34} - 12q^{35} + 28q^{37} - 8q^{38} + 6q^{39} - 4q^{40} + 2q^{41} + 6q^{42} - 6q^{43} - 12q^{45} + 4q^{46} + 16q^{47} + 6q^{48} - 5q^{49} + 11q^{50} + 7q^{51} - 6q^{52} + 10q^{53} + 8q^{56} - 5q^{57} - 4q^{58} + q^{59} + 8q^{60} - 8q^{61} + 2q^{62} - 16q^{63} - 9q^{64} - 16q^{65} - 94q^{67} - 2q^{68} + 2q^{69} + 16q^{70} + 4q^{71} - 7q^{72} + 14q^{73} + 18q^{74} + 31q^{75} + 10q^{76} - 16q^{78} + 30q^{79} - 2q^{80} + 19q^{82} + 19q^{83} - 8q^{84} - 2q^{85} - 11q^{86} + 20q^{87} - 54q^{89} - 12q^{90} - 52q^{91} - 2q^{92} - 62q^{93} - 12q^{94} + 10q^{95} + 4q^{96} - 57q^{97} + 12q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(242, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
242.2.c.a \(4\) \(1.932\) \(\Q(\zeta_{10})\) None \(-1\) \(1\) \(4\) \(2\) \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
242.2.c.b \(4\) \(1.932\) \(\Q(\zeta_{10})\) None \(-1\) \(2\) \(3\) \(2\) \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
242.2.c.c \(4\) \(1.932\) \(\Q(\zeta_{10})\) None \(1\) \(-4\) \(-6\) \(-2\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(-\zeta_{10}+\cdots)q^{3}+\cdots\)
242.2.c.d \(4\) \(1.932\) \(\Q(\zeta_{10})\) None \(1\) \(1\) \(4\) \(-2\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+(\zeta_{10}+\cdots)q^{3}+\cdots\)
242.2.c.e \(4\) \(1.932\) \(\Q(\zeta_{10})\) None \(1\) \(2\) \(3\) \(-2\) \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-2\zeta_{10}^{2}q^{3}+\cdots\)
242.2.c.f \(8\) \(1.932\) 8.0.324000000.3 None \(-2\) \(2\) \(0\) \(-6\) \(q+(-1-\beta _{2}-\beta _{4}-\beta _{6})q^{2}+(-\beta _{1}+\cdots)q^{3}+\cdots\)
242.2.c.g \(8\) \(1.932\) 8.0.324000000.3 None \(2\) \(2\) \(0\) \(6\) \(q-\beta _{4}q^{2}+(-\beta _{2}-\beta _{7})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(242, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(242, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 2}\)