Properties

Label 1368.2.s
Level $1368$
Weight $2$
Character orbit 1368.s
Rep. character $\chi_{1368}(505,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $50$
Newform subspaces $13$
Sturm bound $480$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1368.s (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 13 \)
Sturm bound: \(480\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1368, [\chi])\).

Total New Old
Modular forms 512 50 462
Cusp forms 448 50 398
Eisenstein series 64 0 64

Trace form

\( 50 q + 4 q^{7} + O(q^{10}) \) \( 50 q + 4 q^{7} + 2 q^{11} + 4 q^{17} + q^{19} + 2 q^{23} - 21 q^{25} - 8 q^{29} - 16 q^{31} - 12 q^{35} + 8 q^{37} - 7 q^{41} + 6 q^{43} - 12 q^{47} + 26 q^{49} + 4 q^{53} - 10 q^{55} + 25 q^{59} + 52 q^{65} - 23 q^{67} + 8 q^{71} - 15 q^{73} - 12 q^{77} - 14 q^{79} + 42 q^{83} - 18 q^{85} + 12 q^{89} + 16 q^{91} - 34 q^{95} + 27 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1368, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1368.2.s.a 1368.s 19.c $2$ $10.924$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-4+4\zeta_{6})q^{5}-3q^{11}-2\zeta_{6}q^{13}+\cdots\)
1368.2.s.b 1368.s 19.c $2$ $10.924$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(-10\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{5}-5q^{7}+4q^{11}-5\zeta_{6}q^{13}+\cdots\)
1368.2.s.c 1368.s 19.c $2$ $10.924$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-2\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{5}+3q^{7}-6q^{11}+\zeta_{6}q^{13}+\cdots\)
1368.2.s.d 1368.s 19.c $2$ $10.924$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q+3q^{7}-2q^{11}-\zeta_{6}q^{13}+(4-4\zeta_{6})q^{17}+\cdots\)
1368.2.s.e 1368.s 19.c $2$ $10.924$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(2\) \(-6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{5}-3q^{7}-5\zeta_{6}q^{13}+(-4+\cdots)q^{17}+\cdots\)
1368.2.s.f 1368.s 19.c $2$ $10.924$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(2\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{5}+3q^{7}+6q^{11}+\zeta_{6}q^{13}+\cdots\)
1368.2.s.g 1368.s 19.c $2$ $10.924$ \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(3-3\zeta_{6})q^{5}+4q^{11}+5\zeta_{6}q^{13}+\cdots\)
1368.2.s.h 1368.s 19.c $4$ $10.924$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(0\) \(0\) \(-2\) \(8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{1}-\beta _{2})q^{5}+(2+\beta _{3})q^{7}+\cdots\)
1368.2.s.i 1368.s 19.c $4$ $10.924$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1}+\beta _{2})q^{5}+\beta _{3}q^{7}+(-3+\beta _{3})q^{11}+\cdots\)
1368.2.s.j 1368.s 19.c $6$ $10.924$ \(\Q(\zeta_{18})\) None \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\zeta_{18}^{4}+\zeta_{18}^{5})q^{5}+(1-\zeta_{18}^{5})q^{7}+\cdots\)
1368.2.s.k 1368.s 19.c $6$ $10.924$ 6.0.2696112.1 None \(0\) \(0\) \(1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{5}+(-1-\beta _{2}+\beta _{3})q^{7}+(-1+\cdots)q^{11}+\cdots\)
1368.2.s.l 1368.s 19.c $8$ $10.924$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{3}+\beta _{5})q^{5}+(-1+\beta _{6})q^{7}+(-1+\cdots)q^{11}+\cdots\)
1368.2.s.m 1368.s 19.c $8$ $10.924$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1}+\beta _{3}+\beta _{5})q^{5}+(-1+\beta _{6}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1368, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1368, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(684, [\chi])\)\(^{\oplus 2}\)