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Properties

Label 126.4.d
Level $126$
Weight $4$
Character orbit 126.d
Rep. character $\chi_{126}(125,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $1$
Sturm bound $96$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 126.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(96\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(126, [\chi])\).

Total New Old
Modular forms 80 8 72
Cusp forms 64 8 56
Eisenstein series 16 0 16

Trace form

\( 8 q - 32 q^{4} + 40 q^{7} + O(q^{10}) \) \( 8 q - 32 q^{4} + 40 q^{7} + 128 q^{16} + 480 q^{22} - 40 q^{25} - 160 q^{28} - 160 q^{37} + 1040 q^{43} - 672 q^{46} - 2056 q^{49} + 960 q^{58} - 512 q^{64} - 3680 q^{67} + 960 q^{70} + 448 q^{79} + 6720 q^{85} - 1920 q^{88} - 1920 q^{91} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(126, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
126.4.d.a 126.d 21.c $8$ $7.434$ 8.0.\(\cdots\).6 None 126.4.d.a \(0\) \(0\) \(0\) \(40\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-4q^{4}-\beta _{5}q^{5}+(5+\beta _{7})q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(126, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(126, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)