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Properties

Label 237.2.m
Level $237$
Weight $2$
Character orbit 237.m
Rep. character $\chi_{237}(4,\cdot)$
Character field $\Q(\zeta_{39})$
Dimension $312$
Newform subspaces $2$
Sturm bound $53$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 237 = 3 \cdot 79 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 237.m (of order \(39\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 79 \)
Character field: \(\Q(\zeta_{39})\)
Newform subspaces: \( 2 \)
Sturm bound: \(53\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(237, [\chi])\).

Total New Old
Modular forms 696 312 384
Cusp forms 600 312 288
Eisenstein series 96 0 96

Trace form

\( 312 q - 2 q^{2} + q^{3} + 14 q^{4} + 6 q^{6} + 4 q^{7} - 52 q^{8} + 13 q^{9} + O(q^{10}) \) \( 312 q - 2 q^{2} + q^{3} + 14 q^{4} + 6 q^{6} + 4 q^{7} - 52 q^{8} + 13 q^{9} - 20 q^{10} - 52 q^{11} + 4 q^{12} - 5 q^{13} + 4 q^{14} - 4 q^{15} + 12 q^{16} + 4 q^{17} + 4 q^{18} - 4 q^{19} + 10 q^{20} - 8 q^{21} - 62 q^{22} - 10 q^{23} - 60 q^{24} - 65 q^{25} - 2 q^{27} - 6 q^{28} + 12 q^{29} - 35 q^{31} - 112 q^{32} + 4 q^{33} - 102 q^{34} + 12 q^{35} + 14 q^{36} - 29 q^{37} - 128 q^{38} + 5 q^{39} - 24 q^{40} + 24 q^{41} - 58 q^{42} - q^{43} - 12 q^{44} - 58 q^{46} - 52 q^{47} - 4 q^{48} - 35 q^{49} - 134 q^{50} + 4 q^{51} + 40 q^{52} - 78 q^{53} - 20 q^{54} - 6 q^{55} + 50 q^{56} - 48 q^{57} + 20 q^{58} - 102 q^{59} + 6 q^{60} - 32 q^{61} + 52 q^{62} - 9 q^{63} - 84 q^{64} + 108 q^{65} + 100 q^{66} + 41 q^{67} + 168 q^{68} + 76 q^{69} - 160 q^{70} + 88 q^{71} + 104 q^{72} - 84 q^{73} + 180 q^{74} + 111 q^{75} + 150 q^{76} + 72 q^{78} + 3 q^{79} + 4 q^{80} + 13 q^{81} + 90 q^{82} + 100 q^{83} + 134 q^{84} + 100 q^{85} - 56 q^{86} + 56 q^{87} + 74 q^{88} + 68 q^{89} + 62 q^{90} + 46 q^{91} + 232 q^{92} - 25 q^{93} + 80 q^{94} + 120 q^{95} - 109 q^{97} - 54 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(237, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
237.2.m.a 237.m 79.g $144$ $1.892$ None \(-4\) \(-6\) \(12\) \(0\) $\mathrm{SU}(2)[C_{39}]$
237.2.m.b 237.m 79.g $168$ $1.892$ None \(2\) \(7\) \(-12\) \(4\) $\mathrm{SU}(2)[C_{39}]$

Decomposition of \(S_{2}^{\mathrm{old}}(237, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(237, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(79, [\chi])\)\(^{\oplus 2}\)