Properties

Label 361.2.c
Level $361$
Weight $2$
Character orbit 361.c
Rep. character $\chi_{361}(68,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $42$
Newform subspaces $10$
Sturm bound $63$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 361 = 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 361.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 10 \)
Sturm bound: \(63\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(361, [\chi])\).

Total New Old
Modular forms 82 74 8
Cusp forms 42 42 0
Eisenstein series 40 32 8

Trace form

\( 42 q - 12 q^{4} - q^{5} + 2 q^{7} - 3 q^{9} + O(q^{10}) \) \( 42 q - 12 q^{4} - q^{5} + 2 q^{7} - 3 q^{9} + 2 q^{11} + 6 q^{16} - q^{17} - 28 q^{20} - 4 q^{23} - 8 q^{24} + 14 q^{25} + 16 q^{26} - 4 q^{28} + 16 q^{30} - 5 q^{35} + 16 q^{36} - 24 q^{39} + 30 q^{42} - 5 q^{43} - 12 q^{44} + 10 q^{45} - 7 q^{47} - 56 q^{49} - 14 q^{54} - 9 q^{55} - 28 q^{58} - 5 q^{61} - 6 q^{62} - 11 q^{63} - 72 q^{64} + 42 q^{66} + 20 q^{68} - 9 q^{73} - 12 q^{74} - 14 q^{77} + 18 q^{80} + 47 q^{81} - 10 q^{82} + 16 q^{83} - 15 q^{85} + 20 q^{87} + 56 q^{92} - 8 q^{93} + 12 q^{96} - 21 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(361, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
361.2.c.a 361.c 19.c $2$ $2.883$ \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(-3\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{3}+2\zeta_{6}q^{4}+(-3+3\zeta_{6})q^{5}+\cdots\)
361.2.c.b 361.c 19.c $2$ $2.883$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-19}) \) \(0\) \(0\) \(1\) \(6\) $\mathrm{U}(1)[D_{3}]$ \(q+2\zeta_{6}q^{4}+(1-\zeta_{6})q^{5}+3q^{7}+3\zeta_{6}q^{9}+\cdots\)
361.2.c.c 361.c 19.c $2$ $2.883$ \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(-3\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{3}+2\zeta_{6}q^{4}+(-3+3\zeta_{6})q^{5}+\cdots\)
361.2.c.d 361.c 19.c $4$ $2.883$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(-1\) \(-3\) \(-2\) \(12\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(-2+\beta _{1}-2\beta _{3})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
361.2.c.e 361.c 19.c $4$ $2.883$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(0\) \(-4\) \(-1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-2\beta _{1}+\beta _{3})q^{2}+(-2-2\beta _{3})q^{3}+\cdots\)
361.2.c.f 361.c 19.c $4$ $2.883$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(0\) \(4\) \(-1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-2\beta _{1}+\beta _{3})q^{2}+(2+2\beta _{3})q^{3}+\cdots\)
361.2.c.g 361.c 19.c $4$ $2.883$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(1\) \(3\) \(-2\) \(12\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(2-\beta _{1}+2\beta _{3})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
361.2.c.h 361.c 19.c $6$ $2.883$ \(\Q(\zeta_{18})\) None \(-3\) \(-3\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{18}+\zeta_{18}^{5})q^{2}+(-1+\zeta_{18}+\cdots)q^{3}+\cdots\)
361.2.c.i 361.c 19.c $6$ $2.883$ \(\Q(\zeta_{18})\) None \(3\) \(3\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\zeta_{18}-\zeta_{18}^{3}-\zeta_{18}^{4}+\zeta_{18}^{5})q^{2}+\cdots\)
361.2.c.j 361.c 19.c $8$ $2.883$ 8.0.324000000.2 None \(0\) \(0\) \(4\) \(-16\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{3}q^{2}-\beta _{3}q^{3}+(\beta _{2}+\beta _{4}+\beta _{6})q^{4}+\cdots\)