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Properties

Label 1176.2.k
Level $1176$
Weight $2$
Character orbit 1176.k
Rep. character $\chi_{1176}(881,\cdot)$
Character field $\Q$
Dimension $40$
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.k (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(448\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(5\)

Dimensions

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

Total New Old
Modular forms 256 40 216
Cusp forms 192 40 152
Eisenstein series 64 0 64

Trace form

\( 40 q - 4 q^{9} + O(q^{10}) \) \( 40 q - 4 q^{9} - 8 q^{15} + 44 q^{25} + 20 q^{37} - 20 q^{39} + 36 q^{43} + 36 q^{51} + 40 q^{57} - 12 q^{67} - 56 q^{79} + 20 q^{81} - 48 q^{85} - 64 q^{93} - 36 q^{99} + O(q^{100}) \)

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.k.a 1176.k 21.c $16$ $9.390$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+\beta _{8}q^{5}+\beta _{5}q^{9}-\beta _{6}q^{11}+\cdots\)
1176.2.k.b 1176.k 21.c $24$ $9.390$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$

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

\( S_{2}^{\mathrm{old}}(1176, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 2}\)