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Properties

Label 1445.2.a
Level $1445$
Weight $2$
Character orbit 1445.a
Rep. character $\chi_{1445}(1,\cdot)$
Character field $\Q$
Dimension $91$
Newform subspaces $19$
Sturm bound $306$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1445 = 5 \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1445.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 19 \)
Sturm bound: \(306\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1445))\).

Total New Old
Modular forms 170 91 79
Cusp forms 135 91 44
Eisenstein series 35 0 35

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

\(5\)\(17\)FrickeDim
\(+\)\(+\)$+$\(18\)
\(+\)\(-\)$-$\(27\)
\(-\)\(+\)$-$\(27\)
\(-\)\(-\)$+$\(19\)
Plus space\(+\)\(37\)
Minus space\(-\)\(54\)

Trace form

\( 91 q + q^{2} + 93 q^{4} + q^{5} + 4 q^{6} + 8 q^{7} + 9 q^{8} + 87 q^{9} + O(q^{10}) \) \( 91 q + q^{2} + 93 q^{4} + q^{5} + 4 q^{6} + 8 q^{7} + 9 q^{8} + 87 q^{9} - q^{10} - 4 q^{12} + 6 q^{13} - 12 q^{14} - 4 q^{15} + 101 q^{16} - 7 q^{18} - 4 q^{19} - q^{20} - 8 q^{22} + 4 q^{23} - 8 q^{24} + 91 q^{25} - 2 q^{26} + 12 q^{27} + 12 q^{28} + 10 q^{29} + 8 q^{30} - 11 q^{32} - 36 q^{33} - 4 q^{35} + 121 q^{36} + 10 q^{37} - 4 q^{38} - 4 q^{39} - 9 q^{40} - 14 q^{41} - 12 q^{42} + 12 q^{44} + 5 q^{45} - 24 q^{46} - 24 q^{47} + 24 q^{48} + 103 q^{49} + q^{50} - 6 q^{52} - 26 q^{53} + 20 q^{54} - 12 q^{55} - 16 q^{56} - 2 q^{58} + 6 q^{61} - 8 q^{62} + 12 q^{63} + 89 q^{64} + 10 q^{65} + 4 q^{66} + 20 q^{67} - 24 q^{69} - 12 q^{70} - 4 q^{71} - 31 q^{72} + 26 q^{73} - 18 q^{74} - 32 q^{76} - 32 q^{77} - 36 q^{78} + 8 q^{79} + 15 q^{80} + 43 q^{81} + 6 q^{82} - 32 q^{83} - 36 q^{84} - 8 q^{86} - 28 q^{88} + 14 q^{89} + 23 q^{90} + 4 q^{91} + 8 q^{92} - 4 q^{93} - 4 q^{95} - 12 q^{96} - 2 q^{97} + 21 q^{98} - 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1445))\) 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 17
1445.2.a.a 1445.a 1.a $1$ $11.538$ \(\Q\) None \(0\) \(-2\) \(1\) \(2\) $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-2q^{4}+q^{5}+2q^{7}+q^{9}-3q^{11}+\cdots\)
1445.2.a.b 1445.a 1.a $1$ $11.538$ \(\Q\) None \(0\) \(2\) \(-1\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{4}-q^{5}-2q^{7}+q^{9}+3q^{11}+\cdots\)
1445.2.a.c 1445.a 1.a $1$ $11.538$ \(\Q\) None \(1\) \(-2\) \(1\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}-q^{4}+q^{5}-2q^{6}+2q^{7}+\cdots\)
1445.2.a.d 1445.a 1.a $1$ $11.538$ \(\Q\) None \(1\) \(-1\) \(-1\) \(-5\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}-5q^{7}+\cdots\)
1445.2.a.e 1445.a 1.a $1$ $11.538$ \(\Q\) None \(1\) \(1\) \(1\) \(5\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}+5q^{7}+\cdots\)
1445.2.a.f 1445.a 1.a $2$ $11.538$ \(\Q(\sqrt{2}) \) None \(-2\) \(4\) \(2\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(2+\beta )q^{3}+(1-2\beta )q^{4}+\cdots\)
1445.2.a.g 1445.a 1.a $2$ $11.538$ \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(-2\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1+\beta )q^{3}+q^{4}-q^{5}+(3+\cdots)q^{6}+\cdots\)
1445.2.a.h 1445.a 1.a $2$ $11.538$ \(\Q(\sqrt{17}) \) None \(1\) \(-1\) \(-2\) \(5\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-\beta q^{3}+(2+\beta )q^{4}-q^{5}+(-4+\cdots)q^{6}+\cdots\)
1445.2.a.i 1445.a 1.a $2$ $11.538$ \(\Q(\sqrt{17}) \) None \(1\) \(1\) \(2\) \(-5\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+\beta q^{3}+(2+\beta )q^{4}+q^{5}+(4+\cdots)q^{6}+\cdots\)
1445.2.a.j 1445.a 1.a $3$ $11.538$ 3.3.148.1 None \(1\) \(0\) \(-3\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{4}-q^{5}+\cdots\)
1445.2.a.k 1445.a 1.a $3$ $11.538$ 3.3.148.1 None \(1\) \(0\) \(3\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{4}+q^{5}+\cdots\)
1445.2.a.l 1445.a 1.a $6$ $11.538$ 6.6.1397493.1 None \(-3\) \(-3\) \(6\) \(-6\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}-\beta _{5})q^{2}+(-\beta _{1}+\beta _{4})q^{3}+\cdots\)
1445.2.a.m 1445.a 1.a $6$ $11.538$ 6.6.1397493.1 None \(-3\) \(3\) \(-6\) \(6\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}-\beta _{5})q^{2}+(\beta _{1}-\beta _{4})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
1445.2.a.n 1445.a 1.a $6$ $11.538$ 6.6.7718912.1 None \(2\) \(-4\) \(-6\) \(-8\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{5}q^{2}+(-1+\beta _{1})q^{3}+(1-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
1445.2.a.o 1445.a 1.a $6$ $11.538$ 6.6.7718912.1 None \(2\) \(4\) \(6\) \(8\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{5}q^{2}+(1-\beta _{1})q^{3}+(1-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
1445.2.a.p 1445.a 1.a $12$ $11.538$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-4\) \(-8\) \(12\) \(-16\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1-\beta _{5})q^{3}+(1+\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots\)
1445.2.a.q 1445.a 1.a $12$ $11.538$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-4\) \(8\) \(-12\) \(16\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{5})q^{3}+(1+\beta _{6}+\beta _{7}+\cdots)q^{4}+\cdots\)
1445.2.a.r 1445.a 1.a $12$ $11.538$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(3\) \(-3\) \(-12\) \(-6\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{8}q^{3}+(2+\beta _{2})q^{4}-q^{5}+\cdots\)
1445.2.a.s 1445.a 1.a $12$ $11.538$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(3\) \(3\) \(12\) \(6\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{8}q^{3}+(2+\beta _{2})q^{4}+q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1445))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1445)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(85))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(289))\)\(^{\oplus 2}\)