Properties

Label 1425.2.a
Level $1425$
Weight $2$
Character orbit 1425.a
Rep. character $\chi_{1425}(1,\cdot)$
Character field $\Q$
Dimension $58$
Newform subspaces $26$
Sturm bound $400$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1425 = 3 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1425.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 26 \)
Sturm bound: \(400\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1425))\).

Total New Old
Modular forms 212 58 154
Cusp forms 189 58 131
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.

\(3\)\(5\)\(19\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(6\)
\(+\)\(+\)\(-\)\(-\)\(7\)
\(+\)\(-\)\(+\)\(-\)\(7\)
\(+\)\(-\)\(-\)\(+\)\(9\)
\(-\)\(+\)\(+\)\(-\)\(9\)
\(-\)\(+\)\(-\)\(+\)\(4\)
\(-\)\(-\)\(+\)\(+\)\(5\)
\(-\)\(-\)\(-\)\(-\)\(11\)
Plus space\(+\)\(24\)
Minus space\(-\)\(34\)

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1425))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 5 19
1425.2.a.a \(1\) \(11.379\) \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}-q^{4}+q^{6}+3q^{8}+q^{9}+\cdots\)
1425.2.a.b \(1\) \(11.379\) \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}-q^{4}+q^{6}+3q^{8}+q^{9}+\cdots\)
1425.2.a.c \(1\) \(11.379\) \(\Q\) None \(-1\) \(1\) \(0\) \(-4\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}-q^{4}-q^{6}-4q^{7}+3q^{8}+\cdots\)
1425.2.a.d \(1\) \(11.379\) \(\Q\) None \(-1\) \(1\) \(0\) \(2\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}-q^{4}-q^{6}+2q^{7}+3q^{8}+\cdots\)
1425.2.a.e \(1\) \(11.379\) \(\Q\) None \(-1\) \(1\) \(0\) \(4\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{3}-q^{4}-q^{6}+4q^{7}+3q^{8}+\cdots\)
1425.2.a.f \(1\) \(11.379\) \(\Q\) None \(1\) \(-1\) \(0\) \(-4\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}-q^{4}-q^{6}-4q^{7}-3q^{8}+\cdots\)
1425.2.a.g \(1\) \(11.379\) \(\Q\) None \(1\) \(-1\) \(0\) \(2\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}-q^{4}-q^{6}+2q^{7}-3q^{8}+\cdots\)
1425.2.a.h \(1\) \(11.379\) \(\Q\) None \(1\) \(1\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}-q^{4}+q^{6}-3q^{8}+q^{9}+\cdots\)
1425.2.a.i \(1\) \(11.379\) \(\Q\) None \(2\) \(-1\) \(0\) \(-3\) \(+\) \(+\) \(+\) \(q+2q^{2}-q^{3}+2q^{4}-2q^{6}-3q^{7}+\cdots\)
1425.2.a.j \(1\) \(11.379\) \(\Q\) None \(2\) \(1\) \(0\) \(5\) \(-\) \(+\) \(+\) \(q+2q^{2}+q^{3}+2q^{4}+2q^{6}+5q^{7}+\cdots\)
1425.2.a.k \(2\) \(11.379\) \(\Q(\sqrt{2}) \) None \(-2\) \(-2\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}+(1+\cdots)q^{6}+\cdots\)
1425.2.a.l \(2\) \(11.379\) \(\Q(\sqrt{2}) \) None \(-2\) \(2\) \(0\) \(-4\) \(-\) \(+\) \(-\) \(q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}+(-1+\cdots)q^{6}+\cdots\)
1425.2.a.m \(2\) \(11.379\) \(\Q(\sqrt{5}) \) None \(-1\) \(-2\) \(0\) \(4\) \(+\) \(-\) \(-\) \(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots\)
1425.2.a.n \(2\) \(11.379\) \(\Q(\sqrt{5}) \) None \(-1\) \(2\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots\)
1425.2.a.o \(2\) \(11.379\) \(\Q(\sqrt{3}) \) None \(0\) \(-2\) \(0\) \(2\) \(+\) \(+\) \(-\) \(q+\beta q^{2}-q^{3}+q^{4}-\beta q^{6}+(1+\beta )q^{7}+\cdots\)
1425.2.a.p \(2\) \(11.379\) \(\Q(\sqrt{7}) \) None \(0\) \(2\) \(0\) \(2\) \(-\) \(+\) \(+\) \(q+\beta q^{2}+q^{3}+5q^{4}+\beta q^{6}+(1-\beta )q^{7}+\cdots\)
1425.2.a.q \(2\) \(11.379\) \(\Q(\sqrt{5}) \) None \(1\) \(-2\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots\)
1425.2.a.r \(2\) \(11.379\) \(\Q(\sqrt{5}) \) None \(1\) \(2\) \(0\) \(-4\) \(-\) \(+\) \(-\) \(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots\)
1425.2.a.s \(3\) \(11.379\) 3.3.148.1 None \(-1\) \(3\) \(0\) \(-8\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
1425.2.a.t \(3\) \(11.379\) 3.3.837.1 None \(0\) \(-3\) \(0\) \(0\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
1425.2.a.u \(3\) \(11.379\) 3.3.621.1 None \(0\) \(-3\) \(0\) \(0\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
1425.2.a.v \(3\) \(11.379\) 3.3.621.1 None \(0\) \(3\) \(0\) \(0\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
1425.2.a.w \(3\) \(11.379\) 3.3.837.1 None \(0\) \(3\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
1425.2.a.x \(3\) \(11.379\) 3.3.148.1 None \(1\) \(-3\) \(0\) \(8\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
1425.2.a.y \(7\) \(11.379\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-3\) \(-7\) \(0\) \(-8\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
1425.2.a.z \(7\) \(11.379\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(3\) \(7\) \(0\) \(8\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1425))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1425)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(57))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(285))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(475))\)\(^{\oplus 2}\)