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Properties

Label 1638.2.m
Level $1638$
Weight $2$
Character orbit 1638.m
Rep. character $\chi_{1638}(289,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $92$
Newform subspaces $13$
Sturm bound $672$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1638.m (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 13 \)
Sturm bound: \(672\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1638, [\chi])\).

Total New Old
Modular forms 704 92 612
Cusp forms 640 92 548
Eisenstein series 64 0 64

Trace form

\( 92 q + 92 q^{4} - 2 q^{7} + O(q^{10}) \) \( 92 q + 92 q^{4} - 2 q^{7} - 4 q^{10} + 6 q^{11} - 2 q^{13} + 92 q^{16} - 20 q^{17} + 4 q^{19} + 2 q^{22} + 16 q^{23} - 46 q^{25} + 10 q^{26} - 2 q^{28} - 6 q^{29} + 18 q^{31} + 4 q^{35} + 14 q^{38} - 4 q^{40} - 2 q^{41} - 20 q^{43} + 6 q^{44} + 18 q^{47} + 14 q^{49} + 4 q^{50} - 2 q^{52} + 20 q^{53} - 14 q^{55} + 16 q^{58} + 16 q^{59} - 12 q^{61} + 92 q^{64} - 38 q^{65} - 20 q^{68} + 8 q^{70} - 18 q^{71} - 8 q^{73} - 24 q^{74} + 4 q^{76} + 38 q^{77} + 22 q^{79} + 28 q^{83} - 12 q^{85} - 6 q^{86} + 2 q^{88} - 12 q^{89} - 42 q^{91} + 16 q^{92} - 8 q^{94} + 72 q^{95} - 50 q^{97} - 24 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1638, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1638.2.m.a 1638.m 91.h $2$ $13.079$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(0\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+q^{4}+(2-3\zeta_{6})q^{7}-q^{8}-2\zeta_{6}q^{11}+\cdots\)
1638.2.m.b 1638.m 91.h $2$ $13.079$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(2\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+q^{4}+2\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots\)
1638.2.m.c 1638.m 91.h $2$ $13.079$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-3\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+q^{4}-3\zeta_{6}q^{5}+(-3+2\zeta_{6})q^{7}+\cdots\)
1638.2.m.d 1638.m 91.h $2$ $13.079$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-2\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+q^{4}-2\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots\)
1638.2.m.e 1638.m 91.h $2$ $13.079$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+q^{4}+\zeta_{6}q^{5}+(1+2\zeta_{6})q^{7}+\cdots\)
1638.2.m.f 1638.m 91.h $6$ $13.079$ 6.0.4740147.1 None \(6\) \(0\) \(0\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+q^{4}+(\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5})q^{5}+\cdots\)
1638.2.m.g 1638.m 91.h $8$ $13.079$ 8.0.447703281.1 None \(-8\) \(0\) \(-2\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+q^{4}+(-1+2\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)
1638.2.m.h 1638.m 91.h $8$ $13.079$ 8.0.447703281.1 None \(-8\) \(0\) \(-2\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+q^{4}+(-1+\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots\)
1638.2.m.i 1638.m 91.h $8$ $13.079$ 8.0.6498455769.2 None \(8\) \(0\) \(2\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+q^{4}-\beta _{2}q^{5}+(1+\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
1638.2.m.j 1638.m 91.h $10$ $13.079$ 10.0.\(\cdots\).1 None \(-10\) \(0\) \(2\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+q^{4}+(1+\beta _{6}+\beta _{8}-\beta _{9})q^{5}+\cdots\)
1638.2.m.k 1638.m 91.h $10$ $13.079$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(10\) \(0\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\beta _{4}q^{7}+\cdots\)
1638.2.m.l 1638.m 91.h $16$ $13.079$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-16\) \(0\) \(2\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+q^{4}+\beta _{1}q^{5}+\beta _{5}q^{7}-q^{8}+\cdots\)
1638.2.m.m 1638.m 91.h $16$ $13.079$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(16\) \(0\) \(-2\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+q^{4}-\beta _{1}q^{5}+\beta _{5}q^{7}+q^{8}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1638, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1638, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(182, [\chi])\)\(^{\oplus 3}\)