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Properties

Label 387.4.d
Level $387$
Weight $4$
Character orbit 387.d
Rep. character $\chi_{387}(386,\cdot)$
Character field $\Q$
Dimension $44$
Newform subspaces $3$
Sturm bound $176$
Trace bound $4$

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Defining parameters

Level: \( N \) \(=\) \( 387 = 3^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 387.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 129 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(176\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(387, [\chi])\).

Total New Old
Modular forms 136 44 92
Cusp forms 128 44 84
Eisenstein series 8 0 8

Trace form

\( 44 q + 176 q^{4} + O(q^{10}) \) \( 44 q + 176 q^{4} + 144 q^{10} + 152 q^{13} + 968 q^{16} + 908 q^{25} - 400 q^{31} - 1704 q^{40} + 1192 q^{43} - 2692 q^{49} + 3560 q^{52} + 1464 q^{58} + 4928 q^{64} - 2896 q^{67} - 1264 q^{79} - 2216 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(387, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
387.4.d.a 387.d 129.d $4$ $22.834$ \(\Q(\sqrt{-2}, \sqrt{43})\) \(\Q(\sqrt{-43}) \) 387.4.d.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-8q^{4}+(-4\beta _{1}+\beta _{2})q^{11}-4\beta _{3}q^{13}+\cdots\)
387.4.d.b 387.d 129.d $4$ $22.834$ \(\Q(\sqrt{-2}, \sqrt{21})\) None 387.4.d.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}+13q^{4}-2\beta _{3}q^{5}-4\beta _{2}q^{7}+\cdots\)
387.4.d.c 387.d 129.d $36$ $22.834$ None 387.4.d.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(387, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(387, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(129, [\chi])\)\(^{\oplus 2}\)