Properties

Label 387.2.h
Level $387$
Weight $2$
Character orbit 387.h
Rep. character $\chi_{387}(208,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $34$
Newform subspaces $7$
Sturm bound $88$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 387 = 3^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 387.h (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 43 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 7 \)
Sturm bound: \(88\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 96 38 58
Cusp forms 80 34 46
Eisenstein series 16 4 12

Trace form

\( 34 q + 8 q^{2} + 28 q^{4} + q^{5} + 3 q^{7} + 18 q^{8} + O(q^{10}) \) \( 34 q + 8 q^{2} + 28 q^{4} + q^{5} + 3 q^{7} + 18 q^{8} + q^{10} - 6 q^{11} - 2 q^{13} - 6 q^{14} + 16 q^{16} + 4 q^{17} + q^{19} - 9 q^{20} - 14 q^{22} - 2 q^{23} - 4 q^{25} + 9 q^{26} + 2 q^{28} - 7 q^{29} + q^{31} + 24 q^{32} + 2 q^{34} - 2 q^{35} + 10 q^{37} + 5 q^{38} - 9 q^{40} + 4 q^{41} + 26 q^{43} + 44 q^{44} - 6 q^{46} - 10 q^{47} + 14 q^{49} - 25 q^{50} - 12 q^{52} - 8 q^{53} - 24 q^{55} - 7 q^{56} - 34 q^{58} - 34 q^{59} + 10 q^{61} - 39 q^{62} - 26 q^{64} + 38 q^{65} - 6 q^{67} - 37 q^{68} - 70 q^{70} - 12 q^{71} + 14 q^{73} - 36 q^{74} - 33 q^{76} - 5 q^{77} - 22 q^{79} - 17 q^{80} - 22 q^{82} - 6 q^{83} + 26 q^{85} - 73 q^{86} - 126 q^{88} + 30 q^{89} - 18 q^{91} + 11 q^{92} - 138 q^{94} - q^{95} + 32 q^{97} + 18 q^{98} + O(q^{100}) \)

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.h.a 387.h 43.c $2$ $3.090$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(-1\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}-q^{4}+(-1+\zeta_{6})q^{5}-3\zeta_{6}q^{7}+\cdots\)
387.2.h.b 387.h 43.c $2$ $3.090$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(1\) $\mathrm{U}(1)[D_{3}]$ \(q-2q^{4}+\zeta_{6}q^{7}+7\zeta_{6}q^{13}+4q^{16}+\cdots\)
387.2.h.c 387.h 43.c $2$ $3.090$ \(\Q(\sqrt{-3}) \) None \(4\) \(0\) \(2\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+2q^{2}+2q^{4}+(2-2\zeta_{6})q^{5}-3\zeta_{6}q^{7}+\cdots\)
387.2.h.d 387.h 43.c $4$ $3.090$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(6\) \(0\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{2})q^{2}-3\beta _{2}q^{4}-2\beta _{1}q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots\)
387.2.h.e 387.h 43.c $6$ $3.090$ 6.0.64827.1 None \(-2\) \(0\) \(-1\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+(-1+\beta _{2}-\beta _{3})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots\)
387.2.h.f 387.h 43.c $6$ $3.090$ 6.0.1783323.2 None \(2\) \(0\) \(3\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+(1+\beta _{3})q^{4}+(\beta _{3}+\beta _{4}-\beta _{5})q^{5}+\cdots\)
387.2.h.g 387.h 43.c $12$ $3.090$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-\beta _{6})q^{2}+(2+\beta _{2}+\beta _{4}+\beta _{7}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(387, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(387, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(43, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(129, [\chi])\)\(^{\oplus 2}\)