Properties

Label 525.2.a
Level $525$
Weight $2$
Character orbit 525.a
Rep. character $\chi_{525}(1,\cdot)$
Character field $\Q$
Dimension $20$
Newform subspaces $11$
Sturm bound $160$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 525.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 11 \)
Sturm bound: \(160\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(525))\).

Total New Old
Modular forms 92 20 72
Cusp forms 69 20 49
Eisenstein series 23 0 23

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

\(3\)\(5\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(3\)
\(+\)\(+\)\(-\)\(-\)\(1\)
\(+\)\(-\)\(+\)\(-\)\(3\)
\(+\)\(-\)\(-\)\(+\)\(3\)
\(-\)\(+\)\(+\)\(-\)\(4\)
\(-\)\(-\)\(+\)\(+\)\(1\)
\(-\)\(-\)\(-\)\(-\)\(5\)
Plus space\(+\)\(7\)
Minus space\(-\)\(13\)

Trace form

\( 20q + 24q^{4} + 4q^{6} - 2q^{7} + 20q^{9} + O(q^{10}) \) \( 20q + 24q^{4} + 4q^{6} - 2q^{7} + 20q^{9} - 8q^{11} + 8q^{12} + 8q^{13} - 2q^{14} + 40q^{16} + 8q^{17} + 8q^{19} + 2q^{21} + 24q^{22} - 16q^{23} + 12q^{24} - 16q^{26} - 6q^{28} - 32q^{29} - 32q^{34} + 24q^{36} - 8q^{37} - 8q^{38} + 16q^{39} - 32q^{41} - 2q^{42} - 44q^{44} - 28q^{46} - 16q^{47} + 20q^{49} + 8q^{51} - 8q^{52} + 4q^{54} - 30q^{56} + 8q^{57} - 8q^{59} - 8q^{61} - 24q^{62} - 2q^{63} + 28q^{64} - 8q^{66} + 8q^{68} + 16q^{69} + 8q^{71} + 24q^{73} - 68q^{74} + 40q^{76} - 16q^{78} + 32q^{79} + 20q^{81} + 8q^{82} + 32q^{83} + 6q^{84} + 52q^{86} + 8q^{88} + 8q^{89} + 4q^{91} - 16q^{92} + 8q^{93} + 16q^{94} - 52q^{96} - 8q^{97} - 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(525))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 5 7
525.2.a.a \(1\) \(4.192\) \(\Q\) None \(-1\) \(-1\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}-q^{4}+q^{6}-q^{7}+3q^{8}+\cdots\)
525.2.a.b \(1\) \(4.192\) \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{3}-q^{4}-q^{6}-q^{7}+3q^{8}+\cdots\)
525.2.a.c \(1\) \(4.192\) \(\Q\) None \(1\) \(-1\) \(0\) \(1\) \(+\) \(-\) \(-\) \(q+q^{2}-q^{3}-q^{4}-q^{6}+q^{7}-3q^{8}+\cdots\)
525.2.a.d \(1\) \(4.192\) \(\Q\) None \(1\) \(-1\) \(0\) \(1\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}-q^{4}-q^{6}+q^{7}-3q^{8}+\cdots\)
525.2.a.e \(2\) \(4.192\) \(\Q(\sqrt{5}) \) None \(-3\) \(-2\) \(0\) \(2\) \(+\) \(-\) \(-\) \(q+(-1-\beta )q^{2}-q^{3}+3\beta q^{4}+(1+\beta )q^{6}+\cdots\)
525.2.a.f \(2\) \(4.192\) \(\Q(\sqrt{13}) \) None \(-1\) \(-2\) \(0\) \(-2\) \(+\) \(+\) \(+\) \(q-\beta q^{2}-q^{3}+(1+\beta )q^{4}+\beta q^{6}-q^{7}+\cdots\)
525.2.a.g \(2\) \(4.192\) \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(0\) \(-2\) \(-\) \(+\) \(+\) \(q-\beta q^{2}+q^{3}+3q^{4}-\beta q^{6}-q^{7}-\beta q^{8}+\cdots\)
525.2.a.h \(2\) \(4.192\) \(\Q(\sqrt{13}) \) None \(1\) \(2\) \(0\) \(2\) \(-\) \(-\) \(-\) \(q+\beta q^{2}+q^{3}+(1+\beta )q^{4}+\beta q^{6}+q^{7}+\cdots\)
525.2.a.i \(2\) \(4.192\) \(\Q(\sqrt{5}) \) None \(3\) \(2\) \(0\) \(-2\) \(-\) \(+\) \(+\) \(q+(1+\beta )q^{2}+q^{3}+3\beta q^{4}+(1+\beta )q^{6}+\cdots\)
525.2.a.j \(3\) \(4.192\) 3.3.148.1 None \(-1\) \(3\) \(0\) \(3\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
525.2.a.k \(3\) \(4.192\) 3.3.148.1 None \(1\) \(-3\) \(0\) \(-3\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(525))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(525)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(175))\)\(^{\oplus 2}\)