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

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

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 5 19
1425.2.a.a 1425.a 1.a $1$ $11.379$ \(\Q\) None 57.2.a.c \(-1\) \(-1\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{6}+3q^{8}+q^{9}+\cdots\)
1425.2.a.b 1425.a 1.a $1$ $11.379$ \(\Q\) None 1425.2.a.b \(-1\) \(-1\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{6}+3q^{8}+q^{9}+\cdots\)
1425.2.a.c 1425.a 1.a $1$ $11.379$ \(\Q\) None 285.2.a.c \(-1\) \(1\) \(0\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{6}-4q^{7}+3q^{8}+\cdots\)
1425.2.a.d 1425.a 1.a $1$ $11.379$ \(\Q\) None 285.2.a.b \(-1\) \(1\) \(0\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{6}+2q^{7}+3q^{8}+\cdots\)
1425.2.a.e 1425.a 1.a $1$ $11.379$ \(\Q\) None 1425.2.a.e \(-1\) \(1\) \(0\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{6}+4q^{7}+3q^{8}+\cdots\)
1425.2.a.f 1425.a 1.a $1$ $11.379$ \(\Q\) None 1425.2.a.e \(1\) \(-1\) \(0\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{6}-4q^{7}-3q^{8}+\cdots\)
1425.2.a.g 1425.a 1.a $1$ $11.379$ \(\Q\) None 285.2.a.a \(1\) \(-1\) \(0\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{6}+2q^{7}-3q^{8}+\cdots\)
1425.2.a.h 1425.a 1.a $1$ $11.379$ \(\Q\) None 1425.2.a.b \(1\) \(1\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{6}-3q^{8}+q^{9}+\cdots\)
1425.2.a.i 1425.a 1.a $1$ $11.379$ \(\Q\) None 57.2.a.b \(2\) \(-1\) \(0\) \(-3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}-2q^{6}-3q^{7}+\cdots\)
1425.2.a.j 1425.a 1.a $1$ $11.379$ \(\Q\) None 57.2.a.a \(2\) \(1\) \(0\) \(5\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}+2q^{6}+5q^{7}+\cdots\)
1425.2.a.k 1425.a 1.a $2$ $11.379$ \(\Q(\sqrt{2}) \) None 285.2.a.g \(-2\) \(-2\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}-q^{3}+(1-2\beta )q^{4}+(1+\cdots)q^{6}+\cdots\)
1425.2.a.l 1425.a 1.a $2$ $11.379$ \(\Q(\sqrt{2}) \) None 285.2.a.f \(-2\) \(2\) \(0\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+q^{3}+(1-2\beta )q^{4}+(-1+\cdots)q^{6}+\cdots\)
1425.2.a.m 1425.a 1.a $2$ $11.379$ \(\Q(\sqrt{5}) \) None 1425.2.a.m \(-1\) \(-2\) \(0\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots\)
1425.2.a.n 1425.a 1.a $2$ $11.379$ \(\Q(\sqrt{5}) \) None 1425.2.a.n \(-1\) \(2\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots\)
1425.2.a.o 1425.a 1.a $2$ $11.379$ \(\Q(\sqrt{3}) \) None 285.2.a.e \(0\) \(-2\) \(0\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+q^{4}-\beta q^{6}+(1+\beta )q^{7}+\cdots\)
1425.2.a.p 1425.a 1.a $2$ $11.379$ \(\Q(\sqrt{7}) \) None 285.2.a.d \(0\) \(2\) \(0\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+5q^{4}+\beta q^{6}+(1-\beta )q^{7}+\cdots\)
1425.2.a.q 1425.a 1.a $2$ $11.379$ \(\Q(\sqrt{5}) \) None 1425.2.a.n \(1\) \(-2\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots\)
1425.2.a.r 1425.a 1.a $2$ $11.379$ \(\Q(\sqrt{5}) \) None 1425.2.a.m \(1\) \(2\) \(0\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots\)
1425.2.a.s 1425.a 1.a $3$ $11.379$ 3.3.148.1 None 285.2.c.a \(-1\) \(3\) \(0\) \(-8\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
1425.2.a.t 1425.a 1.a $3$ $11.379$ 3.3.837.1 None 1425.2.a.t \(0\) \(-3\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
1425.2.a.u 1425.a 1.a $3$ $11.379$ 3.3.621.1 None 1425.2.a.u \(0\) \(-3\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
1425.2.a.v 1425.a 1.a $3$ $11.379$ 3.3.621.1 None 1425.2.a.u \(0\) \(3\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
1425.2.a.w 1425.a 1.a $3$ $11.379$ 3.3.837.1 None 1425.2.a.t \(0\) \(3\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
1425.2.a.x 1425.a 1.a $3$ $11.379$ 3.3.148.1 None 285.2.c.a \(1\) \(-3\) \(0\) \(8\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
1425.2.a.y 1425.a 1.a $7$ $11.379$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 285.2.c.b \(-3\) \(-7\) \(0\) \(-8\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
1425.2.a.z 1425.a 1.a $7$ $11.379$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 285.2.c.b \(3\) \(7\) \(0\) \(8\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)

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

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