Properties

Label 363.2.a
Level $363$
Weight $2$
Character orbit 363.a
Rep. character $\chi_{363}(1,\cdot)$
Character field $\Q$
Dimension $19$
Newform subspaces $10$
Sturm bound $88$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 363 = 3 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 363.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(88\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(363))\).

Total New Old
Modular forms 56 19 37
Cusp forms 33 19 14
Eisenstein series 23 0 23

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

\(3\)\(11\)FrickeDim
\(+\)\(+\)\(+\)\(4\)
\(+\)\(-\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(8\)
\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(6\)
Minus space\(-\)\(13\)

Trace form

\( 19 q - q^{2} + q^{3} + 21 q^{4} + 2 q^{5} + q^{6} - 4 q^{7} + 3 q^{8} + 19 q^{9} + 2 q^{10} - q^{12} + 2 q^{13} - 12 q^{14} - 2 q^{15} + 13 q^{16} + 2 q^{17} - q^{18} - 10 q^{20} + 4 q^{21} - 12 q^{23}+ \cdots - 9 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(363))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 11
363.2.a.a 363.a 1.a $1$ $2.899$ \(\Q\) None 363.2.a.a \(-2\) \(-1\) \(4\) \(1\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}+4q^{5}+2q^{6}+\cdots\)
363.2.a.b 363.a 1.a $1$ $2.899$ \(\Q\) None 33.2.a.a \(-1\) \(-1\) \(-2\) \(-4\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}-2q^{5}+q^{6}-4q^{7}+\cdots\)
363.2.a.c 363.a 1.a $1$ $2.899$ \(\Q\) None 363.2.a.a \(2\) \(-1\) \(4\) \(-1\) $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}+4q^{5}-2q^{6}+\cdots\)
363.2.a.d 363.a 1.a $2$ $2.899$ \(\Q(\sqrt{5}) \) None 33.2.e.b \(-3\) \(-2\) \(1\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}+(1-\beta )q^{5}+\cdots\)
363.2.a.e 363.a 1.a $2$ $2.899$ \(\Q(\sqrt{5}) \) None 33.2.e.a \(-1\) \(2\) \(-3\) \(-6\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-2+\beta )q^{5}+\cdots\)
363.2.a.f 363.a 1.a $2$ $2.899$ \(\Q(\sqrt{3}) \) None 363.2.a.f \(0\) \(-2\) \(-6\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+q^{4}-3q^{5}-\beta q^{6}-2\beta q^{7}+\cdots\)
363.2.a.g 363.a 1.a $2$ $2.899$ \(\Q(\sqrt{5}) \) None 363.2.a.g \(0\) \(2\) \(4\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+3q^{4}+2q^{5}-\beta q^{6}+\cdots\)
363.2.a.h 363.a 1.a $2$ $2.899$ \(\Q(\sqrt{5}) \) None 33.2.e.a \(1\) \(2\) \(-3\) \(6\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+(-2+\beta )q^{5}+\cdots\)
363.2.a.i 363.a 1.a $2$ $2.899$ \(\Q(\sqrt{5}) \) None 33.2.e.b \(3\) \(-2\) \(1\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}-q^{3}+3\beta q^{4}+(1-\beta )q^{5}+\cdots\)
363.2.a.j 363.a 1.a $4$ $2.899$ \(\Q(\sqrt{3}, \sqrt{11})\) None 363.2.a.j \(0\) \(4\) \(2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{3})q^{4}-\beta _{3}q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(363))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(363)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 2}\)