Properties

Label 368.2.a
Level $368$
Weight $2$
Character orbit 368.a
Rep. character $\chi_{368}(1,\cdot)$
Character field $\Q$
Dimension $11$
Newform subspaces $9$
Sturm bound $96$
Trace bound $5$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 368 = 2^{4} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 368.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 9 \)
Sturm bound: \(96\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(368))\).

Total New Old
Modular forms 54 11 43
Cusp forms 43 11 32
Eisenstein series 11 0 11

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

\(2\)\(23\)FrickeDim.
\(+\)\(+\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(3\)
\(-\)\(+\)\(-\)\(4\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(4\)
Minus space\(-\)\(7\)

Trace form

\( 11 q + 2 q^{3} - 2 q^{5} + 4 q^{7} + 7 q^{9} + O(q^{10}) \) \( 11 q + 2 q^{3} - 2 q^{5} + 4 q^{7} + 7 q^{9} - 2 q^{13} - 2 q^{17} + 4 q^{19} - 3 q^{23} + 5 q^{25} + 2 q^{27} - 2 q^{29} + 10 q^{31} - 8 q^{33} - 10 q^{37} + 14 q^{39} + 6 q^{41} - 10 q^{45} - 22 q^{47} + 11 q^{49} + 4 q^{51} - 10 q^{53} - 24 q^{55} + 8 q^{57} - 4 q^{59} - 18 q^{61} + 32 q^{63} + 12 q^{65} - 8 q^{67} - 6 q^{71} - 2 q^{73} + 6 q^{75} - 8 q^{77} + 28 q^{79} + 3 q^{81} - 20 q^{83} - 12 q^{85} - 46 q^{87} + 6 q^{89} + 4 q^{91} + 12 q^{93} + 8 q^{95} + 6 q^{97} - 8 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(368))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 23
368.2.a.a $1$ $2.938$ \(\Q\) None \(0\) \(-3\) \(0\) \(2\) $+$ $+$ \(q-3q^{3}+2q^{7}+6q^{9}-5q^{13}-6q^{17}+\cdots\)
368.2.a.b $1$ $2.938$ \(\Q\) None \(0\) \(-1\) \(0\) \(-2\) $-$ $-$ \(q-q^{3}-2q^{7}-2q^{9}-q^{13}-6q^{17}+\cdots\)
368.2.a.c $1$ $2.938$ \(\Q\) None \(0\) \(0\) \(0\) \(-4\) $+$ $+$ \(q-4q^{7}-3q^{9}-6q^{11}-2q^{13}+6q^{17}+\cdots\)
368.2.a.d $1$ $2.938$ \(\Q\) None \(0\) \(0\) \(4\) \(4\) $-$ $+$ \(q+4q^{5}+4q^{7}-3q^{9}-2q^{11}-2q^{13}+\cdots\)
368.2.a.e $1$ $2.938$ \(\Q\) None \(0\) \(1\) \(-4\) \(-2\) $+$ $+$ \(q+q^{3}-4q^{5}-2q^{7}-2q^{9}+4q^{11}+\cdots\)
368.2.a.f $1$ $2.938$ \(\Q\) None \(0\) \(1\) \(-2\) \(4\) $+$ $-$ \(q+q^{3}-2q^{5}+4q^{7}-2q^{9}+2q^{11}+\cdots\)
368.2.a.g $1$ $2.938$ \(\Q\) None \(0\) \(3\) \(-2\) \(4\) $-$ $+$ \(q+3q^{3}-2q^{5}+4q^{7}+6q^{9}-2q^{11}+\cdots\)
368.2.a.h $2$ $2.938$ \(\Q(\sqrt{5}) \) None \(0\) \(0\) \(-2\) \(-2\) $-$ $+$ \(q-\beta q^{3}+(-1-\beta )q^{5}+(-1+\beta )q^{7}+\cdots\)
368.2.a.i $2$ $2.938$ \(\Q(\sqrt{17}) \) None \(0\) \(1\) \(4\) \(0\) $+$ $-$ \(q+\beta q^{3}+2q^{5}+(1+\beta )q^{9}-2\beta q^{11}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(368))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(368)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 2}\)