Properties

Label 1075.2.a
Level $1075$
Weight $2$
Character orbit 1075.a
Rep. character $\chi_{1075}(1,\cdot)$
Character field $\Q$
Dimension $66$
Newform subspaces $20$
Sturm bound $220$
Trace bound $8$

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Defining parameters

Level: \( N \) \(=\) \( 1075 = 5^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1075.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 20 \)
Sturm bound: \(220\)
Trace bound: \(8\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1075))\).

Total New Old
Modular forms 116 66 50
Cusp forms 105 66 39
Eisenstein series 11 0 11

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

\(5\)\(43\)FrickeDim
\(+\)\(+\)$+$\(13\)
\(+\)\(-\)$-$\(19\)
\(-\)\(+\)$-$\(19\)
\(-\)\(-\)$+$\(15\)
Plus space\(+\)\(28\)
Minus space\(-\)\(38\)

Trace form

\( 66 q - q^{2} - 2 q^{3} + 61 q^{4} - 4 q^{7} - 3 q^{8} + 58 q^{9} + O(q^{10}) \) \( 66 q - q^{2} - 2 q^{3} + 61 q^{4} - 4 q^{7} - 3 q^{8} + 58 q^{9} - 11 q^{11} + 8 q^{12} - 5 q^{13} + 51 q^{16} - 3 q^{17} + 11 q^{18} - 10 q^{19} - 6 q^{22} + 5 q^{23} + 8 q^{26} + 4 q^{27} - 12 q^{28} + 20 q^{29} - 23 q^{31} + 13 q^{32} + 6 q^{33} - 4 q^{34} + 29 q^{36} - 34 q^{37} + 44 q^{38} + 2 q^{39} - 11 q^{41} + 64 q^{42} + 2 q^{43} - 18 q^{44} - 6 q^{46} + 12 q^{47} + 60 q^{48} + 38 q^{49} - 2 q^{51} + 44 q^{52} + 7 q^{53} + 20 q^{54} + 12 q^{56} - 32 q^{57} - 26 q^{58} + 8 q^{59} - 12 q^{61} + 18 q^{62} - 16 q^{63} - 5 q^{64} - 56 q^{66} - 33 q^{67} - 8 q^{68} + 18 q^{69} + 22 q^{71} - 3 q^{72} - 12 q^{73} - 18 q^{74} - 88 q^{76} + 16 q^{77} - 36 q^{78} - 32 q^{79} + 42 q^{81} - 20 q^{82} + 9 q^{83} - 64 q^{84} - 5 q^{86} + 24 q^{87} - 40 q^{88} + 34 q^{89} - 56 q^{91} + 6 q^{92} + 10 q^{93} + 72 q^{94} - 8 q^{96} - 65 q^{97} - 37 q^{98} - 51 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1075))\) 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 43
1075.2.a.a 1075.a 1.a $1$ $8.584$ \(\Q\) None \(-2\) \(2\) \(0\) \(-2\) $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{3}+2q^{4}-4q^{6}-2q^{7}+\cdots\)
1075.2.a.b 1075.a 1.a $1$ $8.584$ \(\Q\) None \(-1\) \(2\) \(0\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}-q^{4}-2q^{6}+4q^{7}+3q^{8}+\cdots\)
1075.2.a.c 1075.a 1.a $1$ $8.584$ \(\Q\) None \(0\) \(-2\) \(0\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-2q^{4}+4q^{7}+q^{9}+q^{11}+\cdots\)
1075.2.a.d 1075.a 1.a $1$ $8.584$ \(\Q\) None \(0\) \(0\) \(0\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}+2q^{7}-3q^{9}-q^{11}+q^{13}+\cdots\)
1075.2.a.e 1075.a 1.a $1$ $8.584$ \(\Q\) None \(0\) \(2\) \(0\) \(-4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{4}-4q^{7}+q^{9}+q^{11}+\cdots\)
1075.2.a.f 1075.a 1.a $1$ $8.584$ \(\Q\) None \(1\) \(-2\) \(0\) \(-4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}-q^{4}-2q^{6}-4q^{7}-3q^{8}+\cdots\)
1075.2.a.g 1075.a 1.a $1$ $8.584$ \(\Q\) None \(2\) \(-2\) \(0\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-2q^{3}+2q^{4}-4q^{6}+2q^{7}+\cdots\)
1075.2.a.h 1075.a 1.a $1$ $8.584$ \(\Q\) None \(2\) \(2\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{3}+2q^{4}+4q^{6}+q^{9}+\cdots\)
1075.2.a.i 1075.a 1.a $2$ $8.584$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(0\) \(4\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-\beta q^{3}-2q^{6}+(2+\beta )q^{7}-2\beta q^{8}+\cdots\)
1075.2.a.j 1075.a 1.a $3$ $8.584$ 3.3.169.1 None \(-1\) \(-1\) \(0\) \(-1\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{2}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1075.2.a.k 1075.a 1.a $3$ $8.584$ 3.3.169.1 None \(1\) \(1\) \(0\) \(1\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1}+\beta _{2})q^{2}+\beta _{1}q^{3}+(2-2\beta _{1}+\cdots)q^{4}+\cdots\)
1075.2.a.l 1075.a 1.a $3$ $8.584$ 3.3.321.1 None \(2\) \(-1\) \(0\) \(3\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}-\beta _{1}q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
1075.2.a.m 1075.a 1.a $5$ $8.584$ 5.5.1933097.1 None \(-2\) \(1\) \(0\) \(-5\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(2+\beta _{2})q^{4}+\cdots\)
1075.2.a.n 1075.a 1.a $5$ $8.584$ 5.5.24217.1 None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}-\beta _{2})q^{2}+\beta _{3}q^{3}+(-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
1075.2.a.o 1075.a 1.a $5$ $8.584$ 5.5.24217.1 None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(\beta _{1}+\beta _{2})q^{2}-\beta _{3}q^{3}+(-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
1075.2.a.p 1075.a 1.a $6$ $8.584$ 6.6.32503921.1 None \(-3\) \(-4\) \(0\) \(-8\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-1+\beta _{3})q^{3}+(2+\cdots)q^{4}+\cdots\)
1075.2.a.q 1075.a 1.a $6$ $8.584$ 6.6.282109865.1 None \(-1\) \(-2\) \(0\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(2+\beta _{2})q^{4}+(2+\beta _{4}+\cdots)q^{6}+\cdots\)
1075.2.a.r 1075.a 1.a $6$ $8.584$ 6.6.282109865.1 None \(1\) \(2\) \(0\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(2+\beta _{2})q^{4}+(2+\beta _{4}+\cdots)q^{6}+\cdots\)
1075.2.a.s 1075.a 1.a $7$ $8.584$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-4\) \(-5\) \(0\) \(-3\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(-1+\beta _{5})q^{3}+(1+\cdots)q^{4}+\cdots\)
1075.2.a.t 1075.a 1.a $7$ $8.584$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(4\) \(5\) \(0\) \(3\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1-\beta _{5})q^{3}+(1-\beta _{5}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1075))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1075)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(215))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(43))\)\(^{\oplus 3}\)