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Properties

Label 126.16.d
Level $126$
Weight $16$
Character orbit 126.d
Rep. character $\chi_{126}(125,\cdot)$
Character field $\Q$
Dimension $40$
Newform subspaces $1$
Sturm bound $384$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 16 \)
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: \(384\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(126, [\chi])\).

Total New Old
Modular forms 368 40 328
Cusp forms 352 40 312
Eisenstein series 16 0 16

Trace form

\( 40 q - 655360 q^{4} - 577096 q^{7} + O(q^{10}) \) \( 40 q - 655360 q^{4} - 577096 q^{7} + 10737418240 q^{16} + 15012741120 q^{22} + 240658578520 q^{25} + 9455140864 q^{28} + 19750837888 q^{37} + 1178793607984 q^{43} + 5919750832128 q^{46} - 5977420874696 q^{49} - 9318748028928 q^{58} - 175921860444160 q^{64} + 7832586895808 q^{67} - 4428743147520 q^{70} + 1140596540685728 q^{79} + 43787958301920 q^{85} - 245968750510080 q^{88} + 642048330852192 q^{91} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{16}^{\mathrm{new}}(126, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
126.16.d.a 126.d 21.c $40$ $179.794$ None 126.16.d.a \(0\) \(0\) \(0\) \(-577096\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{16}^{\mathrm{old}}(126, [\chi])\) into lower level spaces

\( S_{16}^{\mathrm{old}}(126, [\chi]) \simeq \) \(S_{16}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)