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 $5$

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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

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

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

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