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Properties

Label 242.2.g
Level $242$
Weight $2$
Character orbit 242.g
Rep. character $\chi_{242}(5,\cdot)$
Character field $\Q(\zeta_{55})$
Dimension $440$
Newform subspaces $2$
Sturm bound $66$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 242 = 2 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 242.g (of order \(55\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 121 \)
Character field: \(\Q(\zeta_{55})\)
Newform subspaces: \( 2 \)
Sturm bound: \(66\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 1400 440 960
Cusp forms 1240 440 800
Eisenstein series 160 0 160

Trace form

\( 440 q + q^{2} + 2 q^{3} + 11 q^{4} + 4 q^{5} - q^{6} - 2 q^{7} + q^{8} - 120 q^{9} + O(q^{10}) \) \( 440 q + q^{2} + 2 q^{3} + 11 q^{4} + 4 q^{5} - q^{6} - 2 q^{7} + q^{8} - 120 q^{9} - 26 q^{10} - 21 q^{11} - 9 q^{12} - 62 q^{13} - 24 q^{14} - 54 q^{15} + 11 q^{16} - 2 q^{17} + 8 q^{18} + 5 q^{19} + 4 q^{20} + 12 q^{21} - 33 q^{22} + 20 q^{23} - q^{24} - 5 q^{25} - 8 q^{26} - 13 q^{27} - 2 q^{28} - 10 q^{29} - 6 q^{30} - 50 q^{31} - 4 q^{32} - 11 q^{33} + 14 q^{34} - 12 q^{35} + 16 q^{36} - 58 q^{37} - 78 q^{38} + 6 q^{39} - 26 q^{40} + 2 q^{41} - 2 q^{42} - 6 q^{43} - 4 q^{44} + 68 q^{45} + 4 q^{46} + 2 q^{48} - 89 q^{49} + 11 q^{50} - 114 q^{51} - 6 q^{52} - 68 q^{53} - 48 q^{55} + 8 q^{56} - 16 q^{57} - 60 q^{58} - 11 q^{59} - 8 q^{61} + 2 q^{62} - 126 q^{63} + 11 q^{64} - 82 q^{65} - 27 q^{66} - 60 q^{67} - 2 q^{68} - 30 q^{69} - 44 q^{70} - 64 q^{71} - 7 q^{72} - 30 q^{73} + 18 q^{74} - 13 q^{75} - 45 q^{76} - 36 q^{77} + 48 q^{78} - 80 q^{79} - 6 q^{80} - 149 q^{81} - 49 q^{82} + 19 q^{83} - 8 q^{84} - 222 q^{85} - 31 q^{86} + 20 q^{87} - 32 q^{88} - 80 q^{89} - 188 q^{90} - 210 q^{91} - 98 q^{92} - 96 q^{93} - 188 q^{94} - 166 q^{95} + 4 q^{96} - 91 q^{97} - 76 q^{98} - 97 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
242.2.g.a 242.g 121.g $200$ $1.932$ None \(-5\) \(10\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{55}]$
242.2.g.b 242.g 121.g $240$ $1.932$ None \(6\) \(-8\) \(5\) \(-2\) $\mathrm{SU}(2)[C_{55}]$

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

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