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Properties

Label 368.4.a
Level $368$
Weight $4$
Character orbit 368.a
Rep. character $\chi_{368}(1,\cdot)$
Character field $\Q$
Dimension $33$
Newform subspaces $14$
Sturm bound $192$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 368 = 2^{4} \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 368.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 14 \)
Sturm bound: \(192\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(368))\).

Total New Old
Modular forms 150 33 117
Cusp forms 138 33 105
Eisenstein series 12 0 12

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
\(+\)\(+\)$+$\(8\)
\(+\)\(-\)$-$\(8\)
\(-\)\(+\)$-$\(7\)
\(-\)\(-\)$+$\(10\)
Plus space\(+\)\(18\)
Minus space\(-\)\(15\)

Trace form

\( 33 q - 6 q^{3} + 2 q^{5} + 36 q^{7} + 317 q^{9} + O(q^{10}) \) \( 33 q - 6 q^{3} + 2 q^{5} + 36 q^{7} + 317 q^{9} - 46 q^{13} - 102 q^{17} + 180 q^{19} + 69 q^{23} + 1015 q^{25} - 150 q^{27} - 142 q^{29} - 54 q^{31} - 408 q^{33} - 192 q^{35} + 330 q^{37} + 30 q^{39} + 98 q^{41} + 768 q^{43} + 90 q^{45} + 266 q^{47} + 849 q^{49} + 1012 q^{51} + 106 q^{53} + 296 q^{55} - 552 q^{57} - 884 q^{59} - 190 q^{61} - 416 q^{63} - 348 q^{65} - 168 q^{67} + 2858 q^{71} - 310 q^{73} - 898 q^{75} - 184 q^{77} - 1764 q^{79} + 3673 q^{81} - 1220 q^{83} - 1588 q^{85} + 674 q^{87} - 830 q^{89} + 2836 q^{91} - 1068 q^{93} + 1352 q^{95} + 466 q^{97} + 6424 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(368))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 23
368.4.a.a 368.a 1.a $1$ $21.713$ \(\Q\) None \(0\) \(-8\) \(-4\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q-8q^{3}-4q^{5}+4q^{7}+37q^{9}-26q^{11}+\cdots\)
368.4.a.b 368.a 1.a $1$ $21.713$ \(\Q\) None \(0\) \(1\) \(-10\) \(12\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-10q^{5}+12q^{7}-26q^{9}+42q^{11}+\cdots\)
368.4.a.c 368.a 1.a $1$ $21.713$ \(\Q\) None \(0\) \(4\) \(22\) \(-8\) $+$ $+$ $\mathrm{SU}(2)$ \(q+4q^{3}+22q^{5}-8q^{7}-11q^{9}+20q^{11}+\cdots\)
368.4.a.d 368.a 1.a $1$ $21.713$ \(\Q\) None \(0\) \(5\) \(-6\) \(8\) $-$ $+$ $\mathrm{SU}(2)$ \(q+5q^{3}-6q^{5}+8q^{7}-2q^{9}-34q^{11}+\cdots\)
368.4.a.e 368.a 1.a $1$ $21.713$ \(\Q\) None \(0\) \(9\) \(-20\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+9q^{3}-20q^{5}-2q^{7}+54q^{9}+52q^{11}+\cdots\)
368.4.a.f 368.a 1.a $2$ $21.713$ \(\Q(\sqrt{73}) \) None \(0\) \(-3\) \(10\) \(-12\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+(6-2\beta )q^{5}+(-8+4\beta )q^{7}+\cdots\)
368.4.a.g 368.a 1.a $2$ $21.713$ \(\Q(\sqrt{41}) \) None \(0\) \(1\) \(10\) \(-6\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+3\beta )q^{3}+(4+2\beta )q^{5}+(-2+\cdots)q^{7}+\cdots\)
368.4.a.h 368.a 1.a $3$ $21.713$ 3.3.28669.1 None \(0\) \(-8\) \(0\) \(-42\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-3-\beta _{2})q^{3}+\beta _{1}q^{5}+(-14+\beta _{1}+\cdots)q^{7}+\cdots\)
368.4.a.i 368.a 1.a $3$ $21.713$ 3.3.761.1 None \(0\) \(-1\) \(16\) \(-18\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+(5+2\beta _{1}+\beta _{2})q^{5}+(-5+\cdots)q^{7}+\cdots\)
368.4.a.j 368.a 1.a $3$ $21.713$ 3.3.761.1 None \(0\) \(3\) \(2\) \(28\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{2})q^{3}+(1-\beta _{1}-\beta _{2})q^{5}+(10+\cdots)q^{7}+\cdots\)
368.4.a.k 368.a 1.a $3$ $21.713$ 3.3.1229.1 None \(0\) \(4\) \(-10\) \(46\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}+(-4-\beta _{1}+3\beta _{2})q^{5}+\cdots\)
368.4.a.l 368.a 1.a $4$ $21.713$ 4.4.334189.1 None \(0\) \(-7\) \(14\) \(-16\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-2-\beta _{2})q^{3}+(3+\beta _{1}-\beta _{3})q^{5}+\cdots\)
368.4.a.m 368.a 1.a $4$ $21.713$ 4.4.2822449.1 None \(0\) \(-5\) \(-2\) \(32\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(-1-\beta _{1}+\beta _{3})q^{5}+\cdots\)
368.4.a.n 368.a 1.a $4$ $21.713$ 4.4.167313.1 None \(0\) \(-1\) \(-20\) \(10\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+(-5+\beta _{2}+\beta _{3})q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(368))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(368)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(184))\)\(^{\oplus 2}\)