Properties

Label 1368.3.o
Level $1368$
Weight $3$
Character orbit 1368.o
Rep. character $\chi_{1368}(721,\cdot)$
Character field $\Q$
Dimension $50$
Newform subspaces $4$
Sturm bound $720$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1368.o (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(720\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1368, [\chi])\).

Total New Old
Modular forms 496 50 446
Cusp forms 464 50 414
Eisenstein series 32 0 32

Trace form

\( 50 q - 16 q^{7} + O(q^{10}) \) \( 50 q - 16 q^{7} + 4 q^{11} + 20 q^{17} + 10 q^{19} - 80 q^{23} + 218 q^{25} + 104 q^{35} - 44 q^{43} - 60 q^{47} + 302 q^{49} + 24 q^{55} - 32 q^{61} - 76 q^{73} - 236 q^{77} - 148 q^{83} - 244 q^{85} + 364 q^{95} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1368, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1368.3.o.a 1368.o 19.b $2$ $37.275$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(-14\) \(22\) $\mathrm{SU}(2)[C_{2}]$ \(q-7q^{5}+11q^{7}-3q^{11}+2\beta q^{13}+\cdots\)
1368.3.o.b 1368.o 19.b $8$ $37.275$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(14\) \(-6\) $\mathrm{SU}(2)[C_{2}]$ \(q+(2+\beta _{4})q^{5}+(-1+\beta _{3})q^{7}+(4+\beta _{4}+\cdots)q^{11}+\cdots\)
1368.3.o.c 1368.o 19.b $20$ $37.275$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{5}+(-1-\beta _{3})q^{7}+(-1-\beta _{1}+\cdots)q^{11}+\cdots\)
1368.3.o.d 1368.o 19.b $20$ $37.275$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{10}q^{5}+(-1+\beta _{3})q^{7}+\beta _{14}q^{11}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(1368, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1368, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(684, [\chi])\)\(^{\oplus 2}\)