Properties

Label 3024.2.k
Level $3024$
Weight $2$
Character orbit 3024.k
Rep. character $\chi_{3024}(1889,\cdot)$
Character field $\Q$
Dimension $64$
Newform subspaces $12$
Sturm bound $1152$
Trace bound $25$

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Defining parameters

Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3024.k (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 21 \)
Character field: \(\Q\)
Newform subspaces: \( 12 \)
Sturm bound: \(1152\)
Trace bound: \(25\)
Distinguishing \(T_p\): \(5\), \(11\), \(13\)

Dimensions

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

Total New Old
Modular forms 612 64 548
Cusp forms 540 64 476
Eisenstein series 72 0 72

Trace form

\( 64 q + 2 q^{7} + 56 q^{25} - 32 q^{43} + 28 q^{67} - 60 q^{79} + 8 q^{85} - 42 q^{91}+O(q^{100}) \) Copy content Toggle raw display

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.k.a 3024.k 21.c $2$ $24.147$ \(\Q(\sqrt{-3}) \) None 756.2.f.a \(0\) \(0\) \(-6\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-3 q^{5}+(-\beta-2)q^{7}+3\beta q^{11}+\cdots\)
3024.2.k.b 3024.k 21.c $2$ $24.147$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) 189.2.c.a \(0\) \(0\) \(0\) \(-1\) $\mathrm{U}(1)[D_{2}]$ \(q+(\beta-1)q^{7}+(2\beta-1)q^{13}+(2\beta-1)q^{19}+\cdots\)
3024.2.k.c 3024.k 21.c $2$ $24.147$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) 756.2.f.b \(0\) \(0\) \(0\) \(5\) $\mathrm{U}(1)[D_{2}]$ \(q+(2+\zeta_{6})q^{7}+(1-2\zeta_{6})q^{13}+(-5+\cdots)q^{19}+\cdots\)
3024.2.k.d 3024.k 21.c $2$ $24.147$ \(\Q(\sqrt{-3}) \) None 756.2.f.a \(0\) \(0\) \(6\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+3 q^{5}+(\beta-2)q^{7}+3\beta q^{11}-2\beta q^{13}+\cdots\)
3024.2.k.e 3024.k 21.c $4$ $24.147$ \(\Q(\zeta_{12})\) None 378.2.d.b \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta_{2} q^{5}+(\beta_1-2)q^{7}+\beta_{3} q^{11}+\cdots\)
3024.2.k.f 3024.k 21.c $4$ $24.147$ \(\Q(\zeta_{12})\) None 378.2.d.c \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q-2\beta_{2} q^{5}+(\beta_1-2)q^{7}+2\beta_{3} q^{11}+\cdots\)
3024.2.k.g 3024.k 21.c $4$ $24.147$ \(\Q(\sqrt{-2}, \sqrt{3})\) None 189.2.c.c \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{5}+(-1-\beta _{3})q^{7}-\beta _{1}q^{11}+\cdots\)
3024.2.k.h 3024.k 21.c $4$ $24.147$ \(\Q(\sqrt{-2}, \sqrt{3})\) None 756.2.f.d \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{5}+(1+\beta _{1})q^{7}+\beta _{3}q^{11}+\beta _{1}q^{13}+\cdots\)
3024.2.k.i 3024.k 21.c $4$ $24.147$ \(\Q(\sqrt{-3}, \sqrt{-5})\) None 189.2.c.b \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{5}+(2-\beta _{2})q^{7}-\beta _{1}q^{11}-2\beta _{2}q^{13}+\cdots\)
3024.2.k.j 3024.k 21.c $4$ $24.147$ \(\Q(\zeta_{12})\) None 378.2.d.a \(0\) \(0\) \(0\) \(10\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta_{3} q^{5}+(-\beta_1+3)q^{7}+(-\beta_{3}+2\beta_{2})q^{11}+\cdots\)
3024.2.k.k 3024.k 21.c $16$ $24.147$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 1512.2.k.a \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{9}q^{5}+\beta _{1}q^{7}+\beta _{10}q^{11}-\beta _{5}q^{13}+\cdots\)
3024.2.k.l 3024.k 21.c $16$ $24.147$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 1512.2.k.b \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{5}+\beta _{12}q^{7}-\beta _{10}q^{11}+(\beta _{4}+\cdots)q^{13}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(3024, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(378, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(756, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1008, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1512, [\chi])\)\(^{\oplus 2}\)