Properties

Label 352.2.a
Level $352$
Weight $2$
Character orbit 352.a
Rep. character $\chi_{352}(1,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $8$
Sturm bound $96$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 352 = 2^{5} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 352.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 8 \)
Sturm bound: \(96\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(352))\).

Total New Old
Modular forms 56 10 46
Cusp forms 41 10 31
Eisenstein series 15 0 15

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

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

Trace form

\( 10 q + 4 q^{5} + 10 q^{9} + O(q^{10}) \) \( 10 q + 4 q^{5} + 10 q^{9} - 12 q^{13} - 12 q^{17} - 2 q^{25} + 20 q^{29} + 4 q^{37} - 12 q^{41} + 12 q^{45} - 6 q^{49} - 20 q^{53} + 16 q^{57} + 4 q^{61} + 8 q^{65} - 8 q^{69} - 28 q^{73} - 6 q^{81} + 24 q^{85} - 52 q^{89} - 40 q^{93} - 20 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(352))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 11
352.2.a.a 352.a 1.a $1$ $2.811$ \(\Q\) None 352.2.a.a \(0\) \(-3\) \(1\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+q^{5}+6q^{9}+q^{11}-6q^{13}+\cdots\)
352.2.a.b 352.a 1.a $1$ $2.811$ \(\Q\) None 352.2.a.b \(0\) \(-1\) \(-3\) \(4\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{5}+4q^{7}-2q^{9}-q^{11}+\cdots\)
352.2.a.c 352.a 1.a $1$ $2.811$ \(\Q\) None 352.2.a.c \(0\) \(-1\) \(1\) \(-4\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-4q^{7}-2q^{9}-q^{11}-2q^{13}+\cdots\)
352.2.a.d 352.a 1.a $1$ $2.811$ \(\Q\) None 352.2.a.b \(0\) \(1\) \(-3\) \(-4\) $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-3q^{5}-4q^{7}-2q^{9}+q^{11}+\cdots\)
352.2.a.e 352.a 1.a $1$ $2.811$ \(\Q\) None 352.2.a.c \(0\) \(1\) \(1\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+4q^{7}-2q^{9}+q^{11}-2q^{13}+\cdots\)
352.2.a.f 352.a 1.a $1$ $2.811$ \(\Q\) None 352.2.a.a \(0\) \(3\) \(1\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+q^{5}+6q^{9}-q^{11}-6q^{13}+\cdots\)
352.2.a.g 352.a 1.a $2$ $2.811$ \(\Q(\sqrt{17}) \) None 352.2.a.g \(0\) \(-1\) \(3\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(2-\beta )q^{5}+(1+\beta )q^{9}-q^{11}+\cdots\)
352.2.a.h 352.a 1.a $2$ $2.811$ \(\Q(\sqrt{17}) \) None 352.2.a.g \(0\) \(1\) \(3\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(2-\beta )q^{5}+(1+\beta )q^{9}+q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(352))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(352)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(176))\)\(^{\oplus 2}\)