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Properties

Label 1008.2.cc
Level $1008$
Weight $2$
Character orbit 1008.cc
Rep. character $\chi_{1008}(209,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $92$
Newform subspaces $4$
Sturm bound $384$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.cc (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(384\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1008, [\chi])\).

Total New Old
Modular forms 408 100 308
Cusp forms 360 92 268
Eisenstein series 48 8 40

Trace form

\( 92 q + q^{7} - 4 q^{9} + O(q^{10}) \) \( 92 q + q^{7} - 4 q^{9} + 6 q^{11} - 2 q^{15} - q^{21} + 6 q^{23} - 40 q^{25} - 30 q^{29} - 8 q^{37} - 14 q^{39} - 10 q^{43} - q^{49} + 24 q^{51} + 16 q^{57} - 7 q^{63} + 18 q^{65} + 2 q^{67} - 27 q^{77} + 2 q^{79} - 12 q^{81} - 12 q^{85} + 30 q^{91} - 26 q^{93} + 84 q^{95} - 38 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1008, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1008.2.cc.a 1008.cc 63.o $12$ $8.049$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{8}q^{3}-\beta _{11}q^{5}+(-\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots\)
1008.2.cc.b 1008.cc 63.o $16$ $8.049$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{9}q^{3}+(-\beta _{9}-\beta _{13}+\beta _{15})q^{5}+\cdots\)
1008.2.cc.c 1008.cc 63.o $16$ $8.049$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(1\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{1}-\beta _{8})q^{3}-\beta _{15}q^{5}+(\beta _{10}-\beta _{12}+\cdots)q^{7}+\cdots\)
1008.2.cc.d 1008.cc 63.o $48$ $8.049$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1008, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)