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Properties

Label 126.10.d
Level $126$
Weight $10$
Character orbit 126.d
Rep. character $\chi_{126}(125,\cdot)$
Character field $\Q$
Dimension $24$
Newform subspaces $1$
Sturm bound $240$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 10 \)
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: \(240\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(126, [\chi])\).

Total New Old
Modular forms 224 24 200
Cusp forms 208 24 184
Eisenstein series 16 0 16

Trace form

\( 24 q - 6144 q^{4} + 11352 q^{7} + O(q^{10}) \) \( 24 q - 6144 q^{4} + 11352 q^{7} + 1572864 q^{16} - 2810880 q^{22} + 5727336 q^{25} - 2906112 q^{28} + 22697664 q^{37} - 37034832 q^{43} - 54125568 q^{46} - 7045176 q^{49} + 277714944 q^{58} - 402653184 q^{64} - 559614336 q^{67} - 234547200 q^{70} + 1451237088 q^{79} - 3592219680 q^{85} + 719585280 q^{88} - 3875613408 q^{91} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(126, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
126.10.d.a 126.d 21.c $24$ $64.895$ None \(0\) \(0\) \(0\) \(11352\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{10}^{\mathrm{old}}(126, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(126, [\chi]) \cong \) \(S_{10}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)