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Properties

Label 1176.2.p
Level $1176$
Weight $2$
Character orbit 1176.p
Rep. character $\chi_{1176}(979,\cdot)$
Character field $\Q$
Dimension $80$
Newform subspaces $2$
Sturm bound $448$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1176.p (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 56 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(448\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1176, [\chi])\).

Total New Old
Modular forms 240 80 160
Cusp forms 208 80 128
Eisenstein series 32 0 32

Trace form

\( 80 q - 4 q^{2} - 4 q^{4} + 8 q^{8} - 80 q^{9} + O(q^{10}) \) \( 80 q - 4 q^{2} - 4 q^{4} + 8 q^{8} - 80 q^{9} + 16 q^{11} - 20 q^{16} + 4 q^{18} - 4 q^{22} + 80 q^{25} + 16 q^{30} + 16 q^{32} + 4 q^{36} + 16 q^{43} + 16 q^{44} - 64 q^{46} + 20 q^{50} + 16 q^{57} - 36 q^{58} - 44 q^{60} - 28 q^{64} + 32 q^{67} - 8 q^{72} + 20 q^{74} + 36 q^{78} + 80 q^{81} - 36 q^{86} - 4 q^{88} - 128 q^{92} - 16 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1176, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1176.2.p.a 1176.p 56.e $32$ $9.390$ None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1176.2.p.b 1176.p 56.e $48$ $9.390$ None \(-8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1176, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1176, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 2}\)