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Properties

Label 361.2.a
Level $361$
Weight $2$
Character orbit 361.a
Rep. character $\chi_{361}(1,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $9$
Sturm bound $63$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 361 = 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 361.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(63\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(361))\).

Total New Old
Modular forms 41 37 4
Cusp forms 22 20 2
Eisenstein series 19 17 2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(19\)TotalCuspEisenstein
AllNewOldAllNewOldAllNewOld
\(+\)\(18\)\(16\)\(2\)\(9\)\(8\)\(1\)\(9\)\(8\)\(1\)
\(-\)\(23\)\(21\)\(2\)\(13\)\(12\)\(1\)\(10\)\(9\)\(1\)

Trace form

\( 20 q + 2 q^{3} + 14 q^{4} - 2 q^{5} + 2 q^{7} + 2 q^{9} - 2 q^{11} - 4 q^{12} + 4 q^{13} + 6 q^{15} - 10 q^{16} + 4 q^{17} - 8 q^{20} - 2 q^{21} + 4 q^{23} + 8 q^{24} - 18 q^{25} + 8 q^{26} - 4 q^{27} + 2 q^{28}+ \cdots + 18 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(361))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 19
361.2.a.a 361.a 1.a $1$ $2.883$ \(\Q\) \(\Q(\sqrt{-19}) \) 361.2.a.a \(0\) \(0\) \(-1\) \(3\) $+$ $N(\mathrm{U}(1))$ \(q-2q^{4}-q^{5}+3q^{7}-3q^{9}-5q^{11}+\cdots\)
361.2.a.b 361.a 1.a $1$ $2.883$ \(\Q\) None 19.2.a.a \(0\) \(2\) \(3\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{4}+3q^{5}-q^{7}+q^{9}+3q^{11}+\cdots\)
361.2.a.c 361.a 1.a $2$ $2.883$ \(\Q(\sqrt{5}) \) None 361.2.a.c \(-1\) \(-3\) \(2\) \(6\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-2+\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
361.2.a.d 361.a 1.a $2$ $2.883$ \(\Q(\sqrt{5}) \) None 361.2.a.d \(0\) \(-4\) \(1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(1-2\beta )q^{2}-2q^{3}+3q^{4}+(1-\beta )q^{5}+\cdots\)
361.2.a.e 361.a 1.a $2$ $2.883$ \(\Q(\sqrt{5}) \) None 361.2.a.d \(0\) \(4\) \(1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(1-2\beta )q^{2}+2q^{3}+3q^{4}+\beta q^{5}+\cdots\)
361.2.a.f 361.a 1.a $2$ $2.883$ \(\Q(\sqrt{5}) \) None 361.2.a.c \(1\) \(3\) \(2\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(2-\beta )q^{3}+(-1+\beta )q^{4}+2\beta q^{5}+\cdots\)
361.2.a.g 361.a 1.a $3$ $2.883$ \(\Q(\zeta_{18})^+\) None 19.2.e.a \(-3\) \(-3\) \(-3\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-1+\beta _{2})q^{3}+(1+\cdots)q^{4}+\cdots\)
361.2.a.h 361.a 1.a $3$ $2.883$ \(\Q(\zeta_{18})^+\) None 19.2.e.a \(3\) \(3\) \(-3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1-\beta _{2})q^{3}+(1-2\beta _{1}+\cdots)q^{4}+\cdots\)
361.2.a.i 361.a 1.a $4$ $2.883$ \(\Q(\zeta_{20})^+\) None 361.2.a.i \(0\) \(0\) \(-4\) \(-8\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{1}q^{3}+(1+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(361))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(361)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 2}\)