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Properties

Label 126.5.b
Level $126$
Weight $5$
Character orbit 126.b
Rep. character $\chi_{126}(71,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $2$
Sturm bound $120$
Trace bound $10$

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Defining parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 126.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(120\)
Trace bound: \(10\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(126, [\chi])\).

Total New Old
Modular forms 104 8 96
Cusp forms 88 8 80
Eisenstein series 16 0 16

Trace form

\( 8 q - 64 q^{4} + O(q^{10}) \) \( 8 q - 64 q^{4} - 128 q^{10} + 560 q^{13} + 512 q^{16} - 1040 q^{19} - 640 q^{22} + 648 q^{25} - 880 q^{31} + 2048 q^{34} - 5120 q^{37} + 1024 q^{40} + 8992 q^{43} - 1792 q^{46} + 2744 q^{49} - 4480 q^{52} - 1168 q^{55} - 2432 q^{58} - 8032 q^{61} - 4096 q^{64} + 14928 q^{67} + 6272 q^{70} - 27360 q^{73} + 8320 q^{76} - 5488 q^{79} + 18432 q^{82} + 32480 q^{85} + 5120 q^{88} + 1568 q^{91} - 39168 q^{94} + 7872 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(126, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
126.5.b.a 126.b 3.b $4$ $13.025$ \(\Q(\sqrt{-2}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2\beta _{1}q^{2}-8q^{4}+(-13\beta _{1}+\beta _{2})q^{5}+\cdots\)
126.5.b.b 126.b 3.b $4$ $13.025$ \(\Q(\sqrt{-2}, \sqrt{7})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2\beta _{1}q^{2}-8q^{4}+(5\beta _{1}+\beta _{2})q^{5}+7\beta _{3}q^{7}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(126, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(126, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)