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Properties

Label 1338.2.e
Level $1338$
Weight $2$
Character orbit 1338.e
Rep. character $\chi_{1338}(931,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $76$
Newform subspaces $10$
Sturm bound $448$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 1338 = 2 \cdot 3 \cdot 223 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1338.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 223 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 10 \)
Sturm bound: \(448\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1338, [\chi])\).

Total New Old
Modular forms 456 76 380
Cusp forms 440 76 364
Eisenstein series 16 0 16

Trace form

\( 76 q + 76 q^{4} + 2 q^{6} + 4 q^{7} - 38 q^{9} + 2 q^{10} - 4 q^{11} - 24 q^{13} + 16 q^{14} - 12 q^{15} + 76 q^{16} + 16 q^{17} - 4 q^{19} + 18 q^{22} + 8 q^{23} + 2 q^{24} - 24 q^{25} + 16 q^{26} + 4 q^{28}+ \cdots - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(1338, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1338.2.e.a 1338.e 223.c $2$ $10.684$ \(\Q(\sqrt{-3}) \) None 1338.2.e.a \(-2\) \(-1\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(-1+\zeta_{6})q^{3}+q^{4}+(1-\zeta_{6})q^{6}+\cdots\)
1338.2.e.b 1338.e 223.c $2$ $10.684$ \(\Q(\sqrt{-3}) \) None 1338.2.e.b \(-2\) \(1\) \(0\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(1-\zeta_{6})q^{3}+q^{4}+(-1+\zeta_{6})q^{6}+\cdots\)
1338.2.e.c 1338.e 223.c $2$ $10.684$ \(\Q(\sqrt{-3}) \) None 1338.2.e.c \(2\) \(1\) \(-1\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(1-\zeta_{6})q^{3}+q^{4}-\zeta_{6}q^{5}+(1+\cdots)q^{6}+\cdots\)
1338.2.e.d 1338.e 223.c $4$ $10.684$ \(\Q(\sqrt{-3}, \sqrt{-23})\) None 1338.2.e.d \(-4\) \(-2\) \(6\) \(-12\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(-1-\beta _{1})q^{3}+q^{4}-3\beta _{1}q^{5}+\cdots\)
1338.2.e.e 1338.e 223.c $4$ $10.684$ \(\Q(\sqrt{-3}, \sqrt{5})\) None 1338.2.e.e \(-4\) \(2\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}-\beta _{3}q^{3}+q^{4}+(1-2\beta _{1}+\beta _{3})q^{5}+\cdots\)
1338.2.e.f 1338.e 223.c $4$ $10.684$ \(\Q(\sqrt{-3}, \sqrt{5})\) None 1338.2.e.f \(4\) \(2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(1+\beta _{3})q^{3}+q^{4}+\beta _{3}q^{5}+(1+\cdots)q^{6}+\cdots\)
1338.2.e.g 1338.e 223.c $12$ $10.684$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None 1338.2.e.g \(-12\) \(6\) \(-3\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+\beta _{3}q^{3}+q^{4}+(-1-\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
1338.2.e.h 1338.e 223.c $14$ $10.684$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None 1338.2.e.h \(-14\) \(-7\) \(-4\) \(12\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}-\beta _{6}q^{3}+q^{4}+(-1+\beta _{2}+\beta _{6}+\cdots)q^{5}+\cdots\)
1338.2.e.i 1338.e 223.c $14$ $10.684$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None 1338.2.e.i \(14\) \(7\) \(3\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+\beta _{6}q^{3}+q^{4}-\beta _{11}q^{5}+\beta _{6}q^{6}+\cdots\)
1338.2.e.j 1338.e 223.c $18$ $10.684$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None 1338.2.e.j \(18\) \(-9\) \(1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(-1-\beta _{4})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1338, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1338, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(223, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(446, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(669, [\chi])\)\(^{\oplus 2}\)