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Properties

Label 455.2.a
Level $455$
Weight $2$
Character orbit 455.a
Rep. character $\chi_{455}(1,\cdot)$
Character field $\Q$
Dimension $23$
Newform subspaces $6$
Sturm bound $112$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 455 = 5 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 455.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 6 \)
Sturm bound: \(112\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(455))\).

Total New Old
Modular forms 60 23 37
Cusp forms 53 23 30
Eisenstein series 7 0 7

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

\(5\)\(7\)\(13\)FrickeDim
\(+\)\(+\)\(+\)$+$\(1\)
\(+\)\(+\)\(-\)$-$\(4\)
\(+\)\(-\)\(+\)$-$\(7\)
\(-\)\(+\)\(+\)$-$\(4\)
\(-\)\(+\)\(-\)$+$\(1\)
\(-\)\(-\)\(-\)$-$\(6\)
Plus space\(+\)\(2\)
Minus space\(-\)\(21\)

Trace form

\( 23 q + 5 q^{2} + 4 q^{3} + 29 q^{4} - q^{5} + 4 q^{6} + 3 q^{7} + 9 q^{8} + 35 q^{9} + O(q^{10}) \) \( 23 q + 5 q^{2} + 4 q^{3} + 29 q^{4} - q^{5} + 4 q^{6} + 3 q^{7} + 9 q^{8} + 35 q^{9} + 5 q^{10} + 4 q^{11} - 4 q^{12} - q^{13} + q^{14} + 4 q^{15} + 45 q^{16} + 14 q^{17} + q^{18} + 28 q^{19} - 7 q^{20} - 4 q^{21} + 12 q^{22} - 8 q^{23} - 12 q^{24} + 23 q^{25} - 3 q^{26} - 8 q^{27} + 21 q^{28} - 6 q^{29} - 12 q^{30} - 7 q^{32} + 48 q^{33} + 10 q^{34} - q^{35} + 41 q^{36} + 10 q^{37} - 36 q^{38} - 4 q^{39} + 33 q^{40} + 38 q^{41} - 12 q^{42} + 12 q^{43} - 36 q^{44} - 13 q^{45} + 8 q^{46} - 32 q^{47} - 68 q^{48} + 23 q^{49} + 5 q^{50} - 8 q^{51} - 7 q^{52} + 2 q^{53} - 56 q^{54} - 12 q^{55} - 3 q^{56} + 32 q^{57} - 26 q^{58} - 28 q^{59} - 4 q^{60} + 26 q^{61} - 40 q^{62} + 23 q^{63} + 61 q^{64} + 7 q^{65} - 80 q^{66} + 44 q^{67} - 14 q^{68} - 32 q^{69} + q^{70} - 75 q^{72} + 86 q^{73} - 42 q^{74} + 4 q^{75} + 36 q^{76} + 4 q^{77} - 4 q^{78} + 16 q^{79} - 31 q^{80} + 95 q^{81} - 30 q^{82} + 12 q^{83} - 28 q^{84} + 22 q^{85} - 76 q^{86} - 40 q^{87} - 36 q^{88} - 42 q^{89} + 9 q^{90} - q^{91} - 88 q^{92} - 32 q^{93} - 48 q^{94} - 12 q^{95} - 140 q^{96} + 30 q^{97} + 5 q^{98} - 76 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(455))\) 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 7 13
455.2.a.a 455.a 1.a $1$ $3.633$ \(\Q\) None \(-1\) \(0\) \(1\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+q^{5}-q^{7}+3q^{8}-3q^{9}+\cdots\)
455.2.a.b 455.a 1.a $1$ $3.633$ \(\Q\) None \(1\) \(0\) \(-1\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-q^{5}-q^{7}-3q^{8}-3q^{9}+\cdots\)
455.2.a.c 455.a 1.a $4$ $3.633$ 4.4.12197.1 None \(-1\) \(0\) \(-4\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
455.2.a.d 455.a 1.a $4$ $3.633$ 4.4.1957.1 None \(3\) \(4\) \(4\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1}+\beta _{2})q^{2}+(1-\beta _{2}-\beta _{3})q^{3}+\cdots\)
455.2.a.e 455.a 1.a $6$ $3.633$ 6.6.45853772.1 None \(3\) \(0\) \(6\) \(6\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{5}q^{3}+(1-\beta _{1}-\beta _{2})q^{4}+\cdots\)
455.2.a.f 455.a 1.a $7$ $3.633$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(0\) \(-7\) \(7\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{6}q^{3}+(2+\beta _{1}+\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(455))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(455)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 2}\)