Properties

Label 1035.2.a
Level $1035$
Weight $2$
Character orbit 1035.a
Rep. character $\chi_{1035}(1,\cdot)$
Character field $\Q$
Dimension $38$
Newform subspaces $17$
Sturm bound $288$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1035 = 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1035.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 17 \)
Sturm bound: \(288\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1035))\).

Total New Old
Modular forms 152 38 114
Cusp forms 137 38 99
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.

\(3\)\(5\)\(23\)FrickeDim
\(+\)\(+\)\(+\)$+$\(2\)
\(+\)\(+\)\(-\)$-$\(6\)
\(+\)\(-\)\(+\)$-$\(6\)
\(+\)\(-\)\(-\)$+$\(2\)
\(-\)\(+\)\(+\)$-$\(5\)
\(-\)\(+\)\(-\)$+$\(6\)
\(-\)\(-\)\(+\)$+$\(3\)
\(-\)\(-\)\(-\)$-$\(8\)
Plus space\(+\)\(13\)
Minus space\(-\)\(25\)

Trace form

\( 38 q + 2 q^{2} + 42 q^{4} + 4 q^{7} + 12 q^{8} + O(q^{10}) \) \( 38 q + 2 q^{2} + 42 q^{4} + 4 q^{7} + 12 q^{8} + 8 q^{11} + 8 q^{13} + 4 q^{14} + 42 q^{16} + 4 q^{17} - 8 q^{19} - 8 q^{20} + 4 q^{22} + 6 q^{23} + 38 q^{25} + 14 q^{26} + 32 q^{28} - 6 q^{29} - 2 q^{31} + 26 q^{32} - 16 q^{34} + 6 q^{35} + 28 q^{37} - 24 q^{38} + 22 q^{41} - 8 q^{43} + 60 q^{44} + 8 q^{47} + 56 q^{49} + 2 q^{50} - 2 q^{52} - 36 q^{53} - 8 q^{55} - 8 q^{56} - 50 q^{58} - 18 q^{59} - 20 q^{61} + 2 q^{62} + 80 q^{64} + 4 q^{65} - 28 q^{67} - 4 q^{68} + 12 q^{70} + 18 q^{71} - 20 q^{73} - 24 q^{74} + 8 q^{76} - 52 q^{77} - 4 q^{79} + 2 q^{82} + 20 q^{83} - 18 q^{85} + 4 q^{86} + 8 q^{88} - 12 q^{89} + 4 q^{91} + 12 q^{92} + 38 q^{94} + 8 q^{95} + 8 q^{97} + 34 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1035))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 5 23
1035.2.a.a 1035.a 1.a $1$ $8.265$ \(\Q\) None \(-2\) \(0\) \(-1\) \(3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}-q^{5}+3q^{7}+2q^{10}+\cdots\)
1035.2.a.b 1035.a 1.a $1$ $8.265$ \(\Q\) None \(-2\) \(0\) \(1\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+q^{5}+q^{7}-2q^{10}+\cdots\)
1035.2.a.c 1035.a 1.a $1$ $8.265$ \(\Q\) None \(-1\) \(0\) \(1\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+q^{5}+4q^{7}+3q^{8}-q^{10}+\cdots\)
1035.2.a.d 1035.a 1.a $1$ $8.265$ \(\Q\) None \(0\) \(0\) \(1\) \(-3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}+q^{5}-3q^{7}+4q^{11}+4q^{16}+\cdots\)
1035.2.a.e 1035.a 1.a $1$ $8.265$ \(\Q\) None \(0\) \(0\) \(1\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}+q^{5}+q^{7}-4q^{11}+4q^{16}+\cdots\)
1035.2.a.f 1035.a 1.a $1$ $8.265$ \(\Q\) None \(1\) \(0\) \(1\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+q^{5}+4q^{7}-3q^{8}+q^{10}+\cdots\)
1035.2.a.g 1035.a 1.a $1$ $8.265$ \(\Q\) None \(2\) \(0\) \(-1\) \(-5\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-q^{5}-5q^{7}-2q^{10}+\cdots\)
1035.2.a.h 1035.a 1.a $2$ $8.265$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{5}+(-1+\beta )q^{7}-2\beta q^{8}+\cdots\)
1035.2.a.i 1035.a 1.a $2$ $8.265$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{5}+(-1-\beta )q^{7}-2\beta q^{8}+\cdots\)
1035.2.a.j 1035.a 1.a $2$ $8.265$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{5}+(-1+2\beta )q^{7}-2\beta q^{8}+\cdots\)
1035.2.a.k 1035.a 1.a $2$ $8.265$ \(\Q(\sqrt{6}) \) None \(0\) \(0\) \(2\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+4q^{4}+q^{5}-q^{7}+2\beta q^{8}+\cdots\)
1035.2.a.l 1035.a 1.a $2$ $8.265$ \(\Q(\sqrt{3}) \) None \(2\) \(0\) \(-2\) \(-6\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(2+2\beta )q^{4}-q^{5}-3q^{7}+\cdots\)
1035.2.a.m 1035.a 1.a $2$ $8.265$ \(\Q(\sqrt{5}) \) None \(3\) \(0\) \(2\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+3\beta q^{4}+q^{5}+(-2+2\beta )q^{7}+\cdots\)
1035.2.a.n 1035.a 1.a $3$ $8.265$ 3.3.316.1 None \(1\) \(0\) \(-3\) \(6\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(2+\beta _{2})q^{7}+\cdots\)
1035.2.a.o 1035.a 1.a $4$ $8.265$ 4.4.15317.1 None \(-2\) \(0\) \(-4\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}-q^{5}+(-1+\cdots)q^{7}+\cdots\)
1035.2.a.p 1035.a 1.a $6$ $8.265$ 6.6.98838128.1 None \(0\) \(0\) \(-6\) \(6\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+(2+\beta _{4})q^{4}-q^{5}+(1+\beta _{3}+\cdots)q^{7}+\cdots\)
1035.2.a.q 1035.a 1.a $6$ $8.265$ 6.6.98838128.1 None \(0\) \(0\) \(6\) \(6\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+(2+\beta _{4})q^{4}+q^{5}+(1+\beta _{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1035))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1035)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(207))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(345))\)\(^{\oplus 2}\)