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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3024.2.q.a \(2\) \(24.147\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-3\) \(4\) \(q+(-3+3\zeta_{6})q^{5}+(3-2\zeta_{6})q^{7}+3\zeta_{6}q^{11}+\cdots\)
3024.2.q.b \(2\) \(24.147\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(-4\) \(q+(-1+\zeta_{6})q^{5}+(-3+2\zeta_{6})q^{7}-5\zeta_{6}q^{11}+\cdots\)
3024.2.q.c \(2\) \(24.147\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-1\) \(4\) \(q+(-1+\zeta_{6})q^{5}+(3-2\zeta_{6})q^{7}-3\zeta_{6}q^{11}+\cdots\)
3024.2.q.d \(2\) \(24.147\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(1\) \(-4\) \(q+(1-\zeta_{6})q^{5}+(-1-2\zeta_{6})q^{7}+3\zeta_{6}q^{11}+\cdots\)
3024.2.q.e \(2\) \(24.147\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(2\) \(5\) \(q+(2-2\zeta_{6})q^{5}+(2+\zeta_{6})q^{7}-4\zeta_{6}q^{11}+\cdots\)
3024.2.q.f \(2\) \(24.147\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(4\) \(q+(3-3\zeta_{6})q^{5}+(1+2\zeta_{6})q^{7}+3\zeta_{6}q^{11}+\cdots\)
3024.2.q.g \(6\) \(24.147\) 6.0.309123.1 None \(0\) \(0\) \(-1\) \(-2\) \(q-\beta _{2}q^{5}+(-\beta _{3}-\beta _{4}+\beta _{5})q^{7}+(\beta _{2}+\cdots)q^{11}+\cdots\)
3024.2.q.h \(6\) \(24.147\) 6.0.309123.1 None \(0\) \(0\) \(5\) \(-4\) \(q+(2-2\beta _{4}+\beta _{5})q^{5}+(-1-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
3024.2.q.i \(10\) \(24.147\) 10.0.\(\cdots\).1 None \(0\) \(0\) \(-4\) \(4\) \(q+(-1+\beta _{2}-\beta _{6})q^{5}+(1-\beta _{1}+\beta _{5}+\cdots)q^{7}+\cdots\)
3024.2.q.j \(14\) \(24.147\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(0\) \(0\) \(2\) \(-6\) \(q-\beta _{3}q^{5}+(-\beta _{5}-\beta _{12})q^{7}-\beta _{13}q^{11}+\cdots\)
3024.2.q.k \(22\) \(24.147\) None \(0\) \(0\) \(-3\) \(5\)
3024.2.q.l \(22\) \(24.147\) None \(0\) \(0\) \(-1\) \(-5\)

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

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