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Properties

Label 176.2.m
Level $176$
Weight $2$
Character orbit 176.m
Rep. character $\chi_{176}(49,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $20$
Newform subspaces $4$
Sturm bound $48$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 176 = 2^{4} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 176.m (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 4 \)
Sturm bound: \(48\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(176, [\chi])\).

Total New Old
Modular forms 120 28 92
Cusp forms 72 20 52
Eisenstein series 48 8 40

Trace form

\( 20 q + 3 q^{3} - 3 q^{5} + q^{7} - 10 q^{9} + O(q^{10}) \) \( 20 q + 3 q^{3} - 3 q^{5} + q^{7} - 10 q^{9} + 2 q^{11} - 3 q^{13} + 3 q^{15} - 7 q^{17} + 9 q^{19} - 2 q^{21} + 16 q^{23} - 12 q^{25} + 3 q^{27} + 5 q^{29} + 3 q^{31} + 5 q^{33} - 13 q^{35} - 15 q^{37} - 47 q^{39} + 13 q^{41} - 36 q^{43} + 8 q^{45} - 9 q^{47} + 2 q^{49} - 27 q^{51} - 23 q^{53} - 21 q^{55} + 13 q^{57} + 7 q^{59} - 11 q^{61} - 12 q^{63} - 6 q^{65} + 12 q^{67} - 28 q^{69} + 25 q^{71} - 3 q^{73} + 17 q^{75} + 15 q^{77} + 35 q^{79} + 28 q^{81} + 63 q^{83} + 31 q^{85} + 110 q^{87} - 4 q^{89} + 17 q^{91} + 11 q^{93} + 7 q^{95} + 19 q^{97} + 46 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(176, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
176.2.m.a 176.m 11.c $4$ $1.405$ \(\Q(\zeta_{10})\) None \(0\) \(-3\) \(3\) \(3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{3}+(1+\zeta_{10}^{2}+\cdots)q^{5}+\cdots\)
176.2.m.b 176.m 11.c $4$ $1.405$ \(\Q(\zeta_{10})\) None \(0\) \(1\) \(3\) \(7\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\zeta_{10}+\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+(1+\zeta_{10}^{2}+\cdots)q^{5}+\cdots\)
176.2.m.c 176.m 11.c $4$ $1.405$ \(\Q(\zeta_{10})\) None \(0\) \(4\) \(-6\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\zeta_{10}-2\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+(-2+\cdots)q^{5}+\cdots\)
176.2.m.d 176.m 11.c $8$ $1.405$ 8.0.682515625.5 None \(0\) \(1\) \(-3\) \(-7\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\beta _{1}-\beta _{4}+\beta _{6})q^{3}+(\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(176, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(176, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 2}\)