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Properties

Label 3024.2.q
Level $3024$
Weight $2$
Character orbit 3024.q
Rep. character $\chi_{3024}(2305,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $92$
Newform subspaces $12$
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.q (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 12 \)
Sturm bound: \(1152\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(11\)

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

\( 92 q - q^{5} + q^{7} + O(q^{10}) \) \( 92 q - q^{5} + q^{7} + q^{11} - 2 q^{13} + 2 q^{17} + 2 q^{19} + q^{23} - 37 q^{25} + 6 q^{29} + 14 q^{31} - 9 q^{35} - 2 q^{37} + 2 q^{41} - 4 q^{43} - 42 q^{47} - q^{49} + 2 q^{53} + 18 q^{55} + 70 q^{59} - 2 q^{61} - 2 q^{65} + 2 q^{67} - 32 q^{71} - 2 q^{73} - 21 q^{77} + 2 q^{79} - 28 q^{83} + 3 q^{85} - 2 q^{89} - 4 q^{91} + 54 q^{95} - 2 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3024.2.q.a 3024.q 63.h $2$ $24.147$ \(\Q(\sqrt{-3}) \) None 126.2.e.b \(0\) \(0\) \(-3\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-3+3\zeta_{6})q^{5}+(3-2\zeta_{6})q^{7}+3\zeta_{6}q^{11}+\cdots\)
3024.2.q.b 3024.q 63.h $2$ $24.147$ \(\Q(\sqrt{-3}) \) None 63.2.g.a \(0\) \(0\) \(-1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{5}+(-3+2\zeta_{6})q^{7}-5\zeta_{6}q^{11}+\cdots\)
3024.2.q.c 3024.q 63.h $2$ $24.147$ \(\Q(\sqrt{-3}) \) None 504.2.q.b \(0\) \(0\) \(-1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{5}+(3-2\zeta_{6})q^{7}-3\zeta_{6}q^{11}+\cdots\)
3024.2.q.d 3024.q 63.h $2$ $24.147$ \(\Q(\sqrt{-3}) \) None 504.2.q.a \(0\) \(0\) \(1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{5}+(-1-2\zeta_{6})q^{7}+3\zeta_{6}q^{11}+\cdots\)
3024.2.q.e 3024.q 63.h $2$ $24.147$ \(\Q(\sqrt{-3}) \) None 252.2.i.a \(0\) \(0\) \(2\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{5}+(2+\zeta_{6})q^{7}-4\zeta_{6}q^{11}+\cdots\)
3024.2.q.f 3024.q 63.h $2$ $24.147$ \(\Q(\sqrt{-3}) \) None 126.2.e.a \(0\) \(0\) \(3\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(3-3\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}+3\zeta_{6}q^{11}+\cdots\)
3024.2.q.g 3024.q 63.h $6$ $24.147$ 6.0.309123.1 None 126.2.e.c \(0\) \(0\) \(-1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{5}+(-\beta _{3}-\beta _{4}+\beta _{5})q^{7}+(\beta _{2}+\cdots)q^{11}+\cdots\)
3024.2.q.h 3024.q 63.h $6$ $24.147$ 6.0.309123.1 None 126.2.e.d \(0\) \(0\) \(5\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\beta _{4}+\beta _{5})q^{5}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
3024.2.q.i 3024.q 63.h $10$ $24.147$ 10.0.\(\cdots\).1 None 63.2.g.b \(0\) \(0\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{2}-\beta _{6})q^{5}+(1-\beta _{1}+\beta _{5}+\cdots)q^{7}+\cdots\)
3024.2.q.j 3024.q 63.h $14$ $24.147$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None 252.2.i.b \(0\) \(0\) \(2\) \(-6\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{3}q^{5}+(-\beta _{5}-\beta _{12})q^{7}-\beta _{13}q^{11}+\cdots\)
3024.2.q.k 3024.q 63.h $22$ $24.147$ None 504.2.q.d \(0\) \(0\) \(-3\) \(5\) $\mathrm{SU}(2)[C_{3}]$
3024.2.q.l 3024.q 63.h $22$ $24.147$ None 504.2.q.c \(0\) \(0\) \(-1\) \(-5\) $\mathrm{SU}(2)[C_{3}]$

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

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