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Properties

Label 1602.2.a
Level $1602$
Weight $2$
Character orbit 1602.a
Rep. character $\chi_{1602}(1,\cdot)$
Character field $\Q$
Dimension $38$
Newform subspaces $14$
Sturm bound $540$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 1602 = 2 \cdot 3^{2} \cdot 89 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1602.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 14 \)
Sturm bound: \(540\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1602))\).

Total New Old
Modular forms 278 38 240
Cusp forms 263 38 225
Eisenstein series 15 0 15

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

\(2\)\(3\)\(89\)FrickeDim
\(+\)\(+\)\(+\)$+$\(2\)
\(+\)\(+\)\(-\)$-$\(6\)
\(+\)\(-\)\(+\)$-$\(5\)
\(+\)\(-\)\(-\)$+$\(6\)
\(-\)\(+\)\(+\)$-$\(6\)
\(-\)\(+\)\(-\)$+$\(2\)
\(-\)\(-\)\(+\)$+$\(3\)
\(-\)\(-\)\(-\)$-$\(8\)
Plus space\(+\)\(13\)
Minus space\(-\)\(25\)

Trace form

\( 38 q + 38 q^{4} - 4 q^{5} + O(q^{10}) \) \( 38 q + 38 q^{4} - 4 q^{5} + 4 q^{10} + 2 q^{13} + 38 q^{16} + 14 q^{19} - 4 q^{20} + 12 q^{23} + 54 q^{25} + 6 q^{26} + 2 q^{29} + 8 q^{31} + 16 q^{34} + 12 q^{35} + 14 q^{37} + 10 q^{38} + 4 q^{40} + 16 q^{41} + 6 q^{43} - 8 q^{47} + 50 q^{49} + 16 q^{50} + 2 q^{52} - 28 q^{53} + 8 q^{55} - 2 q^{58} - 6 q^{59} - 6 q^{61} - 12 q^{62} + 38 q^{64} + 12 q^{65} + 32 q^{67} - 4 q^{70} + 8 q^{71} - 8 q^{73} + 26 q^{74} + 14 q^{76} + 8 q^{77} - 4 q^{80} + 12 q^{82} + 6 q^{83} - 6 q^{86} + 6 q^{89} + 4 q^{91} + 12 q^{92} + 44 q^{95} + 16 q^{97} + 20 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1602))\) 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 3 89
1602.2.a.a 1602.a 1.a $1$ $12.792$ \(\Q\) None \(-1\) \(0\) \(-3\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-3q^{5}-4q^{7}-q^{8}+3q^{10}+\cdots\)
1602.2.a.b 1602.a 1.a $1$ $12.792$ \(\Q\) None \(-1\) \(0\) \(2\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}-2q^{7}-q^{8}-2q^{10}+\cdots\)
1602.2.a.c 1602.a 1.a $1$ $12.792$ \(\Q\) None \(1\) \(0\) \(-2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{5}+q^{8}-2q^{10}-4q^{13}+\cdots\)
1602.2.a.d 1602.a 1.a $2$ $12.792$ \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(-1\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-\beta q^{5}+2\beta q^{7}-q^{8}+\beta q^{10}+\cdots\)
1602.2.a.e 1602.a 1.a $2$ $12.792$ \(\Q(\sqrt{5}) \) None \(-2\) \(0\) \(1\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta q^{5}-2q^{7}-q^{8}-\beta q^{10}+\cdots\)
1602.2.a.f 1602.a 1.a $2$ $12.792$ \(\Q(\sqrt{13}) \) None \(2\) \(0\) \(-3\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-1-\beta )q^{5}+(-2+2\beta )q^{7}+\cdots\)
1602.2.a.g 1602.a 1.a $2$ $12.792$ \(\Q(\sqrt{5}) \) None \(2\) \(0\) \(-1\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-\beta q^{5}-2q^{7}+q^{8}-\beta q^{10}+\cdots\)
1602.2.a.h 1602.a 1.a $2$ $12.792$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(2\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(1+2\beta )q^{5}-2q^{7}+q^{8}+\cdots\)
1602.2.a.i 1602.a 1.a $2$ $12.792$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(4\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{5}+(2+\beta )q^{7}+q^{8}+\cdots\)
1602.2.a.j 1602.a 1.a $3$ $12.792$ 3.3.568.1 None \(-3\) \(0\) \(1\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-\beta _{2}q^{5}+(\beta _{1}+\beta _{2})q^{7}+\cdots\)
1602.2.a.k 1602.a 1.a $4$ $12.792$ 4.4.5225.1 None \(-4\) \(0\) \(-1\) \(4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-\beta _{1}+\beta _{3})q^{5}+(1+\beta _{3})q^{7}+\cdots\)
1602.2.a.l 1602.a 1.a $4$ $12.792$ 4.4.106168.1 None \(4\) \(0\) \(-3\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(-1-\beta _{2})q^{5}+(1-\beta _{1}+\cdots)q^{7}+\cdots\)
1602.2.a.m 1602.a 1.a $6$ $12.792$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(-6\) \(0\) \(-3\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-1+\beta _{1})q^{5}+(1-\beta _{4}+\cdots)q^{7}+\cdots\)
1602.2.a.n 1602.a 1.a $6$ $12.792$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(6\) \(0\) \(3\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(1-\beta _{1})q^{5}+(1-\beta _{4})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1602))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1602)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(89))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(178))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(267))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(534))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(801))\)\(^{\oplus 2}\)