Properties

Label 176.4.a
Level $176$
Weight $4$
Character orbit 176.a
Rep. character $\chi_{176}(1,\cdot)$
Character field $\Q$
Dimension $15$
Newform subspaces $10$
Sturm bound $96$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 176 = 2^{4} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 176.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 10 \)
Sturm bound: \(96\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(176))\).

Total New Old
Modular forms 78 15 63
Cusp forms 66 15 51
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.

\(2\)\(11\)FrickeDim
\(+\)\(+\)$+$\(5\)
\(+\)\(-\)$-$\(2\)
\(-\)\(+\)$-$\(4\)
\(-\)\(-\)$+$\(4\)
Plus space\(+\)\(9\)
Minus space\(-\)\(6\)

Trace form

\( 15 q - 6 q^{3} + 2 q^{5} + 36 q^{7} + 135 q^{9} + O(q^{10}) \) \( 15 q - 6 q^{3} + 2 q^{5} + 36 q^{7} + 135 q^{9} - 33 q^{11} - 46 q^{13} + 66 q^{15} - 26 q^{17} + 204 q^{19} + 136 q^{21} + 138 q^{23} + 397 q^{25} + 138 q^{27} - 198 q^{29} - 318 q^{31} + 228 q^{35} + 330 q^{37} + 120 q^{39} + 118 q^{41} + 336 q^{43} - 350 q^{45} + 848 q^{47} + 375 q^{49} - 44 q^{51} - 286 q^{53} + 220 q^{55} + 680 q^{57} - 1738 q^{59} - 1302 q^{61} - 416 q^{63} + 116 q^{65} - 570 q^{67} - 1544 q^{69} + 390 q^{71} - 154 q^{73} + 1292 q^{75} - 3180 q^{79} + 295 q^{81} - 1448 q^{83} - 1348 q^{85} - 1384 q^{87} + 26 q^{89} + 368 q^{91} - 2136 q^{93} - 2064 q^{95} + 1490 q^{97} - 891 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(176))\) 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 11
176.4.a.a 176.a 1.a $1$ $10.384$ \(\Q\) None \(0\) \(-7\) \(9\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q-7q^{3}+9q^{5}-2q^{7}+22q^{9}+11q^{11}+\cdots\)
176.4.a.b 176.a 1.a $1$ $10.384$ \(\Q\) None \(0\) \(-4\) \(14\) \(8\) $-$ $-$ $\mathrm{SU}(2)$ \(q-4q^{3}+14q^{5}+8q^{7}-11q^{9}+11q^{11}+\cdots\)
176.4.a.c 176.a 1.a $1$ $10.384$ \(\Q\) None \(0\) \(-1\) \(-3\) \(10\) $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{5}+10q^{7}-26q^{9}-11q^{11}+\cdots\)
176.4.a.d 176.a 1.a $1$ $10.384$ \(\Q\) None \(0\) \(1\) \(-7\) \(6\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-7q^{5}+6q^{7}-26q^{9}+11q^{11}+\cdots\)
176.4.a.e 176.a 1.a $1$ $10.384$ \(\Q\) None \(0\) \(5\) \(-7\) \(26\) $-$ $-$ $\mathrm{SU}(2)$ \(q+5q^{3}-7q^{5}+26q^{7}-2q^{9}+11q^{11}+\cdots\)
176.4.a.f 176.a 1.a $1$ $10.384$ \(\Q\) None \(0\) \(7\) \(-19\) \(-14\) $-$ $+$ $\mathrm{SU}(2)$ \(q+7q^{3}-19q^{5}-14q^{7}+22q^{9}-11q^{11}+\cdots\)
176.4.a.g 176.a 1.a $2$ $10.384$ \(\Q(\sqrt{97}) \) None \(0\) \(-9\) \(11\) \(-10\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-4-\beta )q^{3}+(6-\beta )q^{5}+(-8+6\beta )q^{7}+\cdots\)
176.4.a.h 176.a 1.a $2$ $10.384$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(-6\) \(56\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(-3+4\beta )q^{5}+(28+\beta )q^{7}+\cdots\)
176.4.a.i 176.a 1.a $2$ $10.384$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(2\) \(-20\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(1+2\beta )q^{5}+(-10+\beta )q^{7}+\cdots\)
176.4.a.j 176.a 1.a $3$ $10.384$ 3.3.11109.1 None \(0\) \(-2\) \(8\) \(-24\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(3+\beta _{2})q^{5}+(-8+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(176))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(176)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 2}\)