Properties

Label 1224.4.c
Level $1224$
Weight $4$
Character orbit 1224.c
Rep. character $\chi_{1224}(577,\cdot)$
Character field $\Q$
Dimension $68$
Newform subspaces $8$
Sturm bound $864$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 1224 = 2^{3} \cdot 3^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1224.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 17 \)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(864\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(5\), \(47\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1224, [\chi])\).

Total New Old
Modular forms 664 68 596
Cusp forms 632 68 564
Eisenstein series 32 0 32

Trace form

\( 68 q + O(q^{10}) \) \( 68 q - 40 q^{13} + 16 q^{17} + 24 q^{19} - 1684 q^{25} + 208 q^{35} - 424 q^{43} + 504 q^{47} - 4028 q^{49} + 1304 q^{53} + 1176 q^{55} - 1160 q^{59} + 1680 q^{67} + 240 q^{77} + 1744 q^{83} + 2688 q^{85} + 2096 q^{89} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1224, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1224.4.c.a 1224.c 17.b $2$ $72.218$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+9iq^{5}-7iq^{7}+2^{4}iq^{11}+82q^{13}+\cdots\)
1224.4.c.b 1224.c 17.b $6$ $72.218$ 6.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{5}+(\beta _{1}-\beta _{2}-2\beta _{3})q^{7}+(-2\beta _{1}+\cdots)q^{11}+\cdots\)
1224.4.c.c 1224.c 17.b $6$ $72.218$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{5}+(-\beta _{1}+\beta _{2}+\beta _{4})q^{7}+(\beta _{1}+\cdots)q^{11}+\cdots\)
1224.4.c.d 1224.c 17.b $6$ $72.218$ 6.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(3\beta _{1}-\beta _{4})q^{5}+(-2\beta _{1}-\beta _{4}-\beta _{5})q^{7}+\cdots\)
1224.4.c.e 1224.c 17.b $8$ $72.218$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{5}+(-\beta _{1}-\beta _{2}-\beta _{4})q^{7}+(2\beta _{2}+\cdots)q^{11}+\cdots\)
1224.4.c.f 1224.c 17.b $12$ $72.218$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{5}+(\beta _{4}-\beta _{5})q^{7}+(-\beta _{4}+\beta _{6}+\cdots)q^{11}+\cdots\)
1224.4.c.g 1224.c 17.b $14$ $72.218$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{5}+\beta _{6}q^{7}+(-\beta _{1}-\beta _{11})q^{11}+\cdots\)
1224.4.c.h 1224.c 17.b $14$ $72.218$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{5}-\beta _{6}q^{7}+(-\beta _{1}-\beta _{11})q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(1224, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1224, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(102, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(136, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(153, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(204, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(306, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(408, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(612, [\chi])\)\(^{\oplus 2}\)