Properties

Label 2075.2.a
Level $2075$
Weight $2$
Character orbit 2075.a
Rep. character $\chi_{2075}(1,\cdot)$
Character field $\Q$
Dimension $130$
Newform subspaces $15$
Sturm bound $420$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 2075 = 5^{2} \cdot 83 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2075.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 15 \)
Sturm bound: \(420\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2075))\).

Total New Old
Modular forms 216 130 86
Cusp forms 205 130 75
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.

\(5\)\(83\)FrickeDim.
\(+\)\(+\)\(+\)\(22\)
\(+\)\(-\)\(-\)\(40\)
\(-\)\(+\)\(-\)\(40\)
\(-\)\(-\)\(+\)\(28\)
Plus space\(+\)\(50\)
Minus space\(-\)\(80\)

Trace form

\( 130 q + q^{2} + 133 q^{4} + 6 q^{6} + 8 q^{7} + 3 q^{8} + 128 q^{9} + O(q^{10}) \) \( 130 q + q^{2} + 133 q^{4} + 6 q^{6} + 8 q^{7} + 3 q^{8} + 128 q^{9} - 4 q^{11} + 4 q^{12} - 2 q^{13} - 8 q^{14} + 147 q^{16} - 10 q^{17} + 19 q^{18} + 6 q^{19} + 17 q^{21} + 16 q^{22} + 11 q^{23} + 8 q^{24} + 2 q^{26} - 9 q^{27} + 24 q^{28} + 14 q^{29} + 4 q^{31} - 3 q^{32} - 9 q^{33} + 16 q^{34} + 105 q^{36} + 6 q^{37} - 12 q^{38} + 22 q^{39} - 5 q^{41} + 14 q^{42} + 20 q^{43} + 16 q^{44} + 36 q^{46} - 4 q^{47} + 8 q^{48} + 148 q^{49} - 13 q^{51} + 28 q^{52} - 10 q^{53} - 30 q^{54} - 40 q^{56} + 8 q^{57} - 14 q^{58} + 4 q^{59} + 10 q^{61} + 12 q^{62} + 31 q^{63} + 203 q^{64} - 60 q^{66} - 2 q^{67} - 58 q^{68} + 16 q^{69} + 16 q^{71} + 69 q^{72} - 4 q^{73} + 40 q^{74} + 10 q^{76} + 21 q^{77} - 12 q^{78} + 42 q^{79} + 170 q^{81} + 2 q^{82} + 6 q^{83} + 46 q^{84} - 44 q^{86} + 16 q^{87} + 76 q^{88} + 44 q^{91} + 6 q^{92} + 41 q^{93} + 4 q^{94} - 62 q^{96} - 12 q^{97} + 21 q^{98} - 8 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2075))\) 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 83
2075.2.a.a 2075.a 1.a $1$ $16.569$ \(\Q\) None \(-1\) \(-3\) \(0\) \(-1\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-3q^{3}-q^{4}+3q^{6}-q^{7}+3q^{8}+\cdots\)
2075.2.a.b 2075.a 1.a $1$ $16.569$ \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-q^{7}+3q^{8}-3q^{9}+3q^{11}+\cdots\)
2075.2.a.c 2075.a 1.a $1$ $16.569$ \(\Q\) None \(1\) \(0\) \(0\) \(1\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+q^{7}-3q^{8}-3q^{9}+3q^{11}+\cdots\)
2075.2.a.d 2075.a 1.a $1$ $16.569$ \(\Q\) None \(1\) \(1\) \(0\) \(3\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{6}+3q^{7}-3q^{8}+\cdots\)
2075.2.a.e 2075.a 1.a $2$ $16.569$ \(\Q(\sqrt{5}) \) None \(1\) \(1\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1-\beta )q^{3}+(-1+\beta )q^{4}-q^{6}+\cdots\)
2075.2.a.f 2075.a 1.a $6$ $16.569$ 6.6.7783241.1 None \(-2\) \(-3\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-\beta _{2}+\beta _{4})q^{3}+\beta _{2}q^{4}+\cdots\)
2075.2.a.g 2075.a 1.a $6$ $16.569$ 6.6.9059636.1 None \(-1\) \(-1\) \(0\) \(-3\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(\beta _{1}+\beta _{2})q^{2}+\beta _{3}q^{3}+(1-\beta _{5})q^{4}+\cdots\)
2075.2.a.h 2075.a 1.a $7$ $16.569$ 7.7.179711353.1 None \(3\) \(5\) \(0\) \(6\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{6}q^{2}+(1-\beta _{1})q^{3}+(1-\beta _{5}+\beta _{6})q^{4}+\cdots\)
2075.2.a.i 2075.a 1.a $8$ $16.569$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-1\) \(1\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{5}q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\beta _{5}+\cdots)q^{6}+\cdots\)
2075.2.a.j 2075.a 1.a $8$ $16.569$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(1\) \(-1\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{5}q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\beta _{5}+\cdots)q^{6}+\cdots\)
2075.2.a.k 2075.a 1.a $11$ $16.569$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(0\) \(0\) \(0\) \(3\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{7}q^{3}+(2+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
2075.2.a.l 2075.a 1.a $19$ $16.569$ \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None \(0\) \(-1\) \(0\) \(-1\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{9}q^{3}+(2+\beta _{2})q^{4}+\beta _{7}q^{6}+\cdots\)
2075.2.a.m 2075.a 1.a $19$ $16.569$ \(\mathbb{Q}[x]/(x^{19} - \cdots)\) None \(0\) \(1\) \(0\) \(1\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{9}q^{3}+(2+\beta _{2})q^{4}+\beta _{7}q^{6}+\cdots\)
2075.2.a.n 2075.a 1.a $20$ $16.569$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-5\) \(-6\) \(0\) \(-14\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{15}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
2075.2.a.o 2075.a 1.a $20$ $16.569$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(5\) \(6\) \(0\) \(14\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{15}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2075))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2075)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(83))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(415))\)\(^{\oplus 2}\)