Properties

Label 387.2.bb
Level $387$
Weight $2$
Character orbit 387.bb
Rep. character $\chi_{387}(25,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $504$
Newform subspaces $1$
Sturm bound $88$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 387 = 3^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 387.bb (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 387 \)
Character field: \(\Q(\zeta_{21})\)
Newform subspaces: \( 1 \)
Sturm bound: \(88\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(387, [\chi])\).

Total New Old
Modular forms 552 552 0
Cusp forms 504 504 0
Eisenstein series 48 48 0

Trace form

\( 504 q - 7 q^{2} - 9 q^{3} + 35 q^{4} - 12 q^{5} - 4 q^{6} + 4 q^{7} - 16 q^{8} - 27 q^{9} + O(q^{10}) \) \( 504 q - 7 q^{2} - 9 q^{3} + 35 q^{4} - 12 q^{5} - 4 q^{6} + 4 q^{7} - 16 q^{8} - 27 q^{9} - 28 q^{10} - 6 q^{11} - 51 q^{12} - 7 q^{13} + 35 q^{14} - 19 q^{15} + 35 q^{16} - 29 q^{17} - 12 q^{18} - 49 q^{19} - 21 q^{20} + 22 q^{21} - 37 q^{22} - 8 q^{23} - 26 q^{24} + 26 q^{25} - 40 q^{26} - 68 q^{28} - 26 q^{29} + 46 q^{30} - 60 q^{31} + 111 q^{32} + 38 q^{33} - 34 q^{34} - 59 q^{35} - 34 q^{36} - 14 q^{37} + 33 q^{38} + 17 q^{39} - 13 q^{40} - 6 q^{41} - 15 q^{42} - 7 q^{43} - 66 q^{44} - 44 q^{45} - 16 q^{46} - 10 q^{47} - 22 q^{48} - 164 q^{49} - 102 q^{50} + 36 q^{51} + 30 q^{52} - 46 q^{53} - 3 q^{54} - 31 q^{55} + 115 q^{56} - 35 q^{57} - 13 q^{58} - 44 q^{59} + 56 q^{60} + 11 q^{61} - 32 q^{62} + 36 q^{63} - 100 q^{64} + 11 q^{65} - 121 q^{66} - 25 q^{67} + 243 q^{68} - 143 q^{69} + 112 q^{70} - 62 q^{71} - 82 q^{72} - 49 q^{73} + 15 q^{74} + 23 q^{75} - 13 q^{76} + 77 q^{77} - 68 q^{78} + 7 q^{79} + 189 q^{80} - 135 q^{81} - 22 q^{82} - 17 q^{83} + 158 q^{84} - 17 q^{85} + 16 q^{86} - 192 q^{87} - 75 q^{88} - 103 q^{89} + 46 q^{90} - 50 q^{91} - 80 q^{92} + 143 q^{93} - 43 q^{94} - 21 q^{95} - 476 q^{96} - 13 q^{97} - 132 q^{98} + 80 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(387, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
387.2.bb.a 387.bb 387.ab $504$ $3.090$ None \(-7\) \(-9\) \(-12\) \(4\) $\mathrm{SU}(2)[C_{21}]$