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Properties

Label 141.2.e
Level $141$
Weight $2$
Character orbit 141.e
Rep. character $\chi_{141}(4,\cdot)$
Character field $\Q(\zeta_{23})$
Dimension $176$
Newform subspaces $2$
Sturm bound $32$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 141 = 3 \cdot 47 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 141.e (of order \(23\) and degree \(22\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 47 \)
Character field: \(\Q(\zeta_{23})\)
Newform subspaces: \( 2 \)
Sturm bound: \(32\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(141, [\chi])\).

Total New Old
Modular forms 396 176 220
Cusp forms 308 176 132
Eisenstein series 88 0 88

Trace form

\( 176 q - 12 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 12 q^{8} - 8 q^{9} + O(q^{10}) \) \( 176 q - 12 q^{4} - 4 q^{5} - 4 q^{6} - 4 q^{7} - 12 q^{8} - 8 q^{9} - 28 q^{10} - 16 q^{11} - 8 q^{12} - 8 q^{13} - 28 q^{14} - 4 q^{15} - 28 q^{16} - 20 q^{17} - 28 q^{19} - 28 q^{20} - 32 q^{22} - 40 q^{23} - 24 q^{24} - 20 q^{25} - 16 q^{26} - 40 q^{28} - 20 q^{29} - 12 q^{30} - 44 q^{31} - 44 q^{32} - 8 q^{33} - 56 q^{34} - 26 q^{35} - 12 q^{36} + 18 q^{37} + 16 q^{38} - 16 q^{39} + 176 q^{40} + 94 q^{41} - 20 q^{42} + 2 q^{43} + 80 q^{44} - 4 q^{45} + 152 q^{46} + 44 q^{47} - 16 q^{48} + 32 q^{49} + 92 q^{50} - 12 q^{51} + 80 q^{52} - 14 q^{53} - 4 q^{54} + 46 q^{55} + 140 q^{56} - 12 q^{57} - 16 q^{58} - 14 q^{59} - 36 q^{60} - 26 q^{61} - 116 q^{62} - 4 q^{63} - 124 q^{64} - 60 q^{65} - 56 q^{66} - 76 q^{67} - 128 q^{68} - 32 q^{69} - 136 q^{70} - 64 q^{71} - 12 q^{72} - 56 q^{73} - 100 q^{74} - 40 q^{75} - 134 q^{76} - 20 q^{77} + 82 q^{78} + 24 q^{79} + 150 q^{80} - 8 q^{81} - 124 q^{82} + 16 q^{83} + 228 q^{84} + 80 q^{85} + 252 q^{86} + 56 q^{87} + 124 q^{88} + 72 q^{89} + 64 q^{90} - 36 q^{91} + 214 q^{92} + 80 q^{93} + 140 q^{94} + 224 q^{95} + 204 q^{96} + 24 q^{97} + 234 q^{98} + 76 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(141, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
141.2.e.a 141.e 47.c $88$ $1.126$ None \(-2\) \(-4\) \(-4\) \(-2\) $\mathrm{SU}(2)[C_{23}]$
141.2.e.b 141.e 47.c $88$ $1.126$ None \(2\) \(4\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{23}]$

Decomposition of \(S_{2}^{\mathrm{old}}(141, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(141, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(47, [\chi])\)\(^{\oplus 2}\)