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Properties

Label 936.4.a
Level $936$
Weight $4$
Character orbit 936.a
Rep. character $\chi_{936}(1,\cdot)$
Character field $\Q$
Dimension $45$
Newform subspaces $17$
Sturm bound $672$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 936.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 17 \)
Sturm bound: \(672\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(936))\).

Total New Old
Modular forms 520 45 475
Cusp forms 488 45 443
Eisenstein series 32 0 32

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

\(2\)\(3\)\(13\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(5\)
\(+\)\(+\)\(-\)\(-\)\(4\)
\(+\)\(-\)\(+\)\(-\)\(6\)
\(+\)\(-\)\(-\)\(+\)\(8\)
\(-\)\(+\)\(+\)\(-\)\(5\)
\(-\)\(+\)\(-\)\(+\)\(4\)
\(-\)\(-\)\(+\)\(+\)\(7\)
\(-\)\(-\)\(-\)\(-\)\(6\)
Plus space\(+\)\(24\)
Minus space\(-\)\(21\)

Trace form

\( 45 q + 10 q^{5} + 12 q^{7} + O(q^{10}) \) \( 45 q + 10 q^{5} + 12 q^{7} - 116 q^{11} - 13 q^{13} + 112 q^{17} + 24 q^{19} + 84 q^{23} + 945 q^{25} + 154 q^{29} - 276 q^{31} - 602 q^{35} - 122 q^{37} - 214 q^{41} + 286 q^{43} + 820 q^{47} + 2491 q^{49} + 134 q^{53} - 2192 q^{55} - 632 q^{59} + 546 q^{61} + 260 q^{65} + 1052 q^{67} + 356 q^{71} + 2782 q^{73} - 464 q^{77} + 124 q^{79} - 2852 q^{83} - 3064 q^{85} + 1058 q^{89} + 546 q^{91} + 4740 q^{95} - 2182 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(936))\) 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 3 13
936.4.a.a 936.a 1.a $1$ $55.226$ \(\Q\) None 104.4.a.b \(0\) \(0\) \(-19\) \(-3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-19q^{5}-3q^{7}+2q^{11}-13q^{13}+\cdots\)
936.4.a.b 936.a 1.a $1$ $55.226$ \(\Q\) None 104.4.a.a \(0\) \(0\) \(7\) \(-21\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+7q^{5}-21q^{7}-6q^{11}+13q^{13}+\cdots\)
936.4.a.c 936.a 1.a $2$ $55.226$ \(\Q(\sqrt{43}) \) None 312.4.a.f \(0\) \(0\) \(-12\) \(44\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-6+\beta )q^{5}+(22-\beta )q^{7}-26q^{11}+\cdots\)
936.4.a.d 936.a 1.a $2$ $55.226$ \(\Q(\sqrt{113}) \) None 312.4.a.c \(0\) \(0\) \(-6\) \(-10\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-3-\beta )q^{5}+(-5-\beta )q^{7}+(8+4\beta )q^{11}+\cdots\)
936.4.a.e 936.a 1.a $2$ $55.226$ \(\Q(\sqrt{73}) \) None 104.4.a.c \(0\) \(0\) \(3\) \(-25\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+3\beta q^{5}+(-12-\beta )q^{7}+(30-4\beta )q^{11}+\cdots\)
936.4.a.f 936.a 1.a $2$ $55.226$ \(\Q(\sqrt{7}) \) None 312.4.a.e \(0\) \(0\) \(4\) \(-20\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{5}+(-10+3\beta )q^{7}+(30+4\beta )q^{11}+\cdots\)
936.4.a.g 936.a 1.a $2$ $55.226$ \(\Q(\sqrt{3}) \) None 312.4.a.a \(0\) \(0\) \(4\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{5}+(2+3\beta )q^{7}+(-14+6\beta )q^{11}+\cdots\)
936.4.a.h 936.a 1.a $2$ $55.226$ \(\Q(\sqrt{55}) \) None 312.4.a.b \(0\) \(0\) \(4\) \(20\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{5}+(10-\beta )q^{7}+(10+2\beta )q^{11}+\cdots\)
936.4.a.i 936.a 1.a $2$ $55.226$ \(\Q(\sqrt{321}) \) None 104.4.a.d \(0\) \(0\) \(11\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(6-\beta )q^{5}+(2-3\beta )q^{7}-58q^{11}+\cdots\)
936.4.a.j 936.a 1.a $2$ $55.226$ \(\Q(\sqrt{17}) \) None 312.4.a.d \(0\) \(0\) \(18\) \(-10\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(9-\beta )q^{5}+(-5-5\beta )q^{7}+(-2-14\beta )q^{11}+\cdots\)
936.4.a.k 936.a 1.a $3$ $55.226$ 3.3.36248.1 None 312.4.a.g \(0\) \(0\) \(-16\) \(-22\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-5-\beta _{2})q^{5}+(-8+\beta _{1}+\beta _{2})q^{7}+\cdots\)
936.4.a.l 936.a 1.a $3$ $55.226$ 3.3.13916.1 None 312.4.a.h \(0\) \(0\) \(4\) \(6\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{2})q^{5}+(2+\beta _{1}+\beta _{2})q^{7}+(-11+\cdots)q^{11}+\cdots\)
936.4.a.m 936.a 1.a $3$ $55.226$ 3.3.18257.1 None 104.4.a.e \(0\) \(0\) \(8\) \(36\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(3+2\beta _{1}+\beta _{2})q^{5}+(12+\beta _{1})q^{7}+\cdots\)
936.4.a.n 936.a 1.a $4$ $55.226$ 4.4.6390848.1 None 936.4.a.n \(0\) \(0\) \(-8\) \(24\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-2-\beta _{1})q^{5}+(6+\beta _{2})q^{7}+(-2^{4}+\cdots)q^{11}+\cdots\)
936.4.a.o 936.a 1.a $4$ $55.226$ 4.4.6390848.1 None 936.4.a.n \(0\) \(0\) \(8\) \(24\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(2+\beta _{1})q^{5}+(6+\beta _{2})q^{7}+(2^{4}-\beta _{1}+\cdots)q^{11}+\cdots\)
936.4.a.p 936.a 1.a $5$ $55.226$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 936.4.a.p \(0\) \(0\) \(-2\) \(-18\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{5}+(-4-\beta _{1})q^{7}+(5+\beta _{1}+2\beta _{2}+\cdots)q^{11}+\cdots\)
936.4.a.q 936.a 1.a $5$ $55.226$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 936.4.a.p \(0\) \(0\) \(2\) \(-18\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{5}+(-4-\beta _{1})q^{7}+(-5-\beta _{1}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(936))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(936)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(78))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(117))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(156))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(234))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(312))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(468))\)\(^{\oplus 2}\)