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Properties

Label 55.6.a
Level $55$
Weight $6$
Character orbit 55.a
Rep. character $\chi_{55}(1,\cdot)$
Character field $\Q$
Dimension $18$
Newform subspaces $4$
Sturm bound $36$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 55 = 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 55.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(36\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(55))\).

Total New Old
Modular forms 32 18 14
Cusp forms 28 18 10
Eisenstein series 4 0 4

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

\(5\)\(11\)FrickeDim
\(+\)\(+\)$+$\(4\)
\(+\)\(-\)$-$\(6\)
\(-\)\(+\)$-$\(5\)
\(-\)\(-\)$+$\(3\)
Plus space\(+\)\(7\)
Minus space\(-\)\(11\)

Trace form

\( 18 q - 36 q^{3} + 332 q^{4} - 50 q^{5} + 32 q^{6} - 188 q^{7} + 852 q^{8} + 2162 q^{9} + O(q^{10}) \) \( 18 q - 36 q^{3} + 332 q^{4} - 50 q^{5} + 32 q^{6} - 188 q^{7} + 852 q^{8} + 2162 q^{9} + 100 q^{10} - 2336 q^{12} - 300 q^{13} + 1480 q^{14} - 900 q^{15} + 6200 q^{16} - 956 q^{17} + 7072 q^{18} - 1912 q^{19} - 500 q^{20} + 128 q^{21} - 968 q^{22} - 5140 q^{23} + 8104 q^{24} + 11250 q^{25} - 18764 q^{26} - 4200 q^{27} - 18180 q^{28} + 13004 q^{29} - 7600 q^{30} + 12280 q^{31} + 46104 q^{32} - 4356 q^{33} - 34632 q^{34} + 3100 q^{35} + 2800 q^{36} - 29116 q^{37} + 6504 q^{38} - 24104 q^{39} + 15600 q^{40} - 22268 q^{41} - 10360 q^{42} + 20172 q^{43} - 2420 q^{44} + 11350 q^{45} + 47384 q^{46} - 3580 q^{47} - 115296 q^{48} + 3906 q^{49} - 20248 q^{51} - 99828 q^{52} - 18396 q^{53} - 72216 q^{54} - 12100 q^{55} + 81528 q^{56} + 52400 q^{57} + 41856 q^{58} + 37920 q^{59} - 83700 q^{60} - 138532 q^{61} - 167776 q^{62} + 274324 q^{63} + 258996 q^{64} + 100 q^{65} + 99220 q^{66} - 44 q^{67} - 142732 q^{68} + 83040 q^{69} + 20500 q^{70} + 101600 q^{71} + 155076 q^{72} + 223908 q^{73} - 53568 q^{74} - 22500 q^{75} - 10048 q^{76} - 17908 q^{77} - 59528 q^{78} - 195328 q^{79} - 45200 q^{80} + 189282 q^{81} + 343952 q^{82} + 328860 q^{83} - 535856 q^{84} + 130500 q^{85} - 59708 q^{86} + 11048 q^{87} - 46464 q^{88} + 118804 q^{89} - 38700 q^{90} + 185440 q^{91} + 314328 q^{92} - 434112 q^{93} + 218032 q^{94} + 91400 q^{95} - 691192 q^{96} + 30852 q^{97} - 476136 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(55))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5 11
55.6.a.a 55.a 1.a $3$ $8.821$ 3.3.21865.1 None \(-7\) \(-36\) \(75\) \(-102\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-2-\beta _{2})q^{2}+(-11-3\beta _{1})q^{3}+\cdots\)
55.6.a.b 55.a 1.a $4$ $8.821$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(-5\) \(0\) \(-100\) \(-90\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{2}+(\beta _{1}-\beta _{3})q^{3}+(15+\cdots)q^{4}+\cdots\)
55.6.a.c 55.a 1.a $5$ $8.821$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(9\) \(0\) \(125\) \(70\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(2-\beta _{1})q^{2}+(\beta _{1}-\beta _{3})q^{3}+(24-3\beta _{1}+\cdots)q^{4}+\cdots\)
55.6.a.d 55.a 1.a $6$ $8.821$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(3\) \(0\) \(-150\) \(-66\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(20+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(55))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(55)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)