Properties

Label 3024.2.cc
Level $3024$
Weight $2$
Character orbit 3024.cc
Rep. character $\chi_{3024}(881,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $92$
Newform subspaces $4$
Sturm bound $1152$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3024.cc (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 4 \)
Sturm bound: \(1152\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3024, [\chi])\).

Total New Old
Modular forms 1224 100 1124
Cusp forms 1080 92 988
Eisenstein series 144 8 136

Trace form

\( 92 q + q^{7} + O(q^{10}) \) \( 92 q + q^{7} - 6 q^{11} - 6 q^{23} - 40 q^{25} + 30 q^{29} - 8 q^{37} - 10 q^{43} - q^{49} - 18 q^{65} + 2 q^{67} + 27 q^{77} + 2 q^{79} - 12 q^{85} + 30 q^{91} - 84 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(3024, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3024.2.cc.a 3024.cc 63.o $12$ $24.147$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{10}q^{5}+(-\beta _{3}+\beta _{4}+\beta _{8}+\beta _{9}+\cdots)q^{7}+\cdots\)
3024.2.cc.b 3024.cc 63.o $16$ $24.147$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{2}-\beta _{9}+\beta _{15})q^{5}-\beta _{14}q^{7}+\cdots\)
3024.2.cc.c 3024.cc 63.o $16$ $24.147$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(1\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}-\beta _{15})q^{5}+(\beta _{6}-\beta _{13})q^{7}+\beta _{5}q^{11}+\cdots\)
3024.2.cc.d 3024.cc 63.o $48$ $24.147$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(3024, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3024, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1512, [\chi])\)\(^{\oplus 2}\)