Properties

Label 4025.2.a
Level $4025$
Weight $2$
Character orbit 4025.a
Rep. character $\chi_{4025}(1,\cdot)$
Character field $\Q$
Dimension $210$
Newform subspaces $31$
Sturm bound $960$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4025.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 31 \)
Sturm bound: \(960\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(3\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4025))\).

Total New Old
Modular forms 492 210 282
Cusp forms 469 210 259
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.

\(5\)\(7\)\(23\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(27\)
\(+\)\(+\)\(-\)\(-\)\(22\)
\(+\)\(-\)\(+\)\(-\)\(31\)
\(+\)\(-\)\(-\)\(+\)\(18\)
\(-\)\(+\)\(+\)\(-\)\(29\)
\(-\)\(+\)\(-\)\(+\)\(27\)
\(-\)\(-\)\(+\)\(+\)\(21\)
\(-\)\(-\)\(-\)\(-\)\(35\)
Plus space\(+\)\(93\)
Minus space\(-\)\(117\)

Trace form

\( 210 q - 4 q^{3} + 212 q^{4} - 10 q^{6} - 6 q^{8} + 206 q^{9} + O(q^{10}) \) \( 210 q - 4 q^{3} + 212 q^{4} - 10 q^{6} - 6 q^{8} + 206 q^{9} - 2 q^{12} + 16 q^{13} + 232 q^{16} + 4 q^{17} + 22 q^{18} - 12 q^{19} + 4 q^{21} + 4 q^{22} - 6 q^{23} + 36 q^{24} - 2 q^{26} - 28 q^{27} - 8 q^{29} - 8 q^{31} - 12 q^{32} - 24 q^{33} - 52 q^{34} + 258 q^{36} + 24 q^{37} + 56 q^{38} + 24 q^{39} - 48 q^{41} + 20 q^{42} + 8 q^{43} + 44 q^{44} + 4 q^{46} + 24 q^{47} + 14 q^{48} + 210 q^{49} - 24 q^{51} + 22 q^{52} + 16 q^{53} - 26 q^{54} - 4 q^{57} + 42 q^{58} - 60 q^{59} + 4 q^{61} + 34 q^{62} + 262 q^{64} + 52 q^{66} + 4 q^{67} + 36 q^{68} + 64 q^{71} + 106 q^{72} + 8 q^{73} - 20 q^{74} - 76 q^{76} - 22 q^{78} + 4 q^{79} + 146 q^{81} - 26 q^{82} - 8 q^{83} + 16 q^{84} - 24 q^{86} + 4 q^{87} + 24 q^{88} - 4 q^{89} + 12 q^{91} - 12 q^{92} - 44 q^{93} + 50 q^{94} + 54 q^{96} + 8 q^{97} + 24 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4025))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5 7 23
4025.2.a.a $1$ $32.140$ \(\Q\) None \(-2\) \(-3\) \(0\) \(1\) $+$ $-$ $+$ \(q-2q^{2}-3q^{3}+2q^{4}+6q^{6}+q^{7}+\cdots\)
4025.2.a.b $1$ $32.140$ \(\Q\) None \(-2\) \(1\) \(0\) \(1\) $+$ $-$ $-$ \(q-2q^{2}+q^{3}+2q^{4}-2q^{6}+q^{7}-2q^{9}+\cdots\)
4025.2.a.c $1$ $32.140$ \(\Q\) None \(0\) \(-1\) \(0\) \(1\) $-$ $-$ $+$ \(q-q^{3}-2q^{4}+q^{7}-2q^{9}-q^{11}+2q^{12}+\cdots\)
4025.2.a.d $1$ $32.140$ \(\Q\) None \(0\) \(1\) \(0\) \(-1\) $-$ $+$ $-$ \(q+q^{3}-2q^{4}-q^{7}-2q^{9}-q^{11}-2q^{12}+\cdots\)
4025.2.a.e $1$ $32.140$ \(\Q\) None \(1\) \(0\) \(0\) \(-1\) $+$ $+$ $-$ \(q+q^{2}-q^{4}-q^{7}-3q^{8}-3q^{9}+4q^{11}+\cdots\)
4025.2.a.f $1$ $32.140$ \(\Q\) None \(1\) \(0\) \(0\) \(1\) $+$ $-$ $+$ \(q+q^{2}-q^{4}+q^{7}-3q^{8}-3q^{9}-4q^{11}+\cdots\)
4025.2.a.g $1$ $32.140$ \(\Q\) None \(1\) \(0\) \(0\) \(1\) $+$ $-$ $+$ \(q+q^{2}-q^{4}+q^{7}-3q^{8}-3q^{9}+2q^{11}+\cdots\)
4025.2.a.h $2$ $32.140$ \(\Q(\sqrt{5}) \) None \(-3\) \(0\) \(0\) \(2\) $+$ $-$ $+$ \(q+(-1-\beta )q^{2}+(-1+2\beta )q^{3}+3\beta q^{4}+\cdots\)
4025.2.a.i $2$ $32.140$ \(\Q(\sqrt{5}) \) None \(1\) \(2\) \(0\) \(2\) $+$ $-$ $-$ \(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots\)
4025.2.a.j $3$ $32.140$ 3.3.148.1 None \(1\) \(-2\) \(0\) \(3\) $+$ $-$ $+$ \(q+(\beta _{1}+\beta _{2})q^{2}+(-1+\beta _{1})q^{3}+(1+2\beta _{1}+\cdots)q^{4}+\cdots\)
4025.2.a.k $3$ $32.140$ \(\Q(\zeta_{14})^+\) None \(2\) \(0\) \(0\) \(3\) $+$ $-$ $-$ \(q+(1-\beta _{1})q^{2}+(-1+\beta _{1}-2\beta _{2})q^{3}+\cdots\)
4025.2.a.l $4$ $32.140$ 4.4.2777.1 None \(-3\) \(-6\) \(0\) \(4\) $+$ $-$ $-$ \(q+(-1+\beta _{1})q^{2}+(-1-\beta _{3})q^{3}+(1+\cdots)q^{4}+\cdots\)
4025.2.a.m $4$ $32.140$ 4.4.7537.1 None \(-1\) \(-4\) \(0\) \(-4\) $+$ $+$ $-$ \(q-\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
4025.2.a.n $4$ $32.140$ 4.4.22545.1 None \(1\) \(0\) \(0\) \(4\) $+$ $-$ $+$ \(q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{3})q^{3}+(3+\beta _{3})q^{4}+\cdots\)
4025.2.a.o $4$ $32.140$ 4.4.2777.1 None \(2\) \(5\) \(0\) \(-4\) $+$ $+$ $-$ \(q+(1-\beta _{3})q^{2}+(1+\beta _{1})q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots\)
4025.2.a.p $5$ $32.140$ 5.5.2147108.1 None \(-2\) \(0\) \(0\) \(-5\) $+$ $+$ $-$ \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(2+\beta _{2})q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots\)
4025.2.a.q $5$ $32.140$ 5.5.255877.1 None \(1\) \(4\) \(0\) \(-5\) $+$ $+$ $+$ \(q+\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
4025.2.a.r $5$ $32.140$ 5.5.122821.1 None \(3\) \(6\) \(0\) \(5\) $+$ $-$ $+$ \(q+(1-\beta _{1})q^{2}+(1+\beta _{3})q^{3}+(\beta _{3}+\beta _{4})q^{4}+\cdots\)
4025.2.a.s $8$ $32.140$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-3\) \(-2\) \(0\) \(8\) $+$ $-$ $-$ \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(\beta _{1}+\beta _{2})q^{4}+(\beta _{6}+\cdots)q^{6}+\cdots\)
4025.2.a.t $8$ $32.140$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-1\) \(-7\) \(0\) \(-8\) $+$ $+$ $+$ \(q-\beta _{1}q^{2}+(-1-\beta _{6})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
4025.2.a.u $8$ $32.140$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-1\) \(-4\) \(0\) \(8\) $-$ $-$ $+$ \(q-\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
4025.2.a.v $8$ $32.140$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(1\) \(4\) \(0\) \(-8\) $+$ $+$ $-$ \(q+\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
4025.2.a.w $8$ $32.140$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(3\) \(2\) \(0\) \(-8\) $-$ $+$ $+$ \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(\beta _{1}+\beta _{2})q^{4}+(\beta _{6}+\cdots)q^{6}+\cdots\)
4025.2.a.x $12$ $32.140$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-2\) \(0\) \(0\) \(12\) $-$ $-$ $+$ \(q-\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
4025.2.a.y $12$ $32.140$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(2\) \(0\) \(0\) \(-12\) $-$ $+$ $-$ \(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
4025.2.a.z $14$ $32.140$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-3\) \(-4\) \(0\) \(-14\) $+$ $+$ $+$ \(q-\beta _{1}q^{2}+\beta _{7}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
4025.2.a.ba $14$ $32.140$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-1\) \(-6\) \(0\) \(-14\) $-$ $+$ $-$ \(q-\beta _{1}q^{2}-\beta _{4}q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
4025.2.a.bb $14$ $32.140$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(1\) \(6\) \(0\) \(14\) $+$ $-$ $+$ \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
4025.2.a.bc $14$ $32.140$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(3\) \(4\) \(0\) \(14\) $-$ $-$ $-$ \(q+\beta _{1}q^{2}-\beta _{7}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
4025.2.a.bd $21$ $32.140$ None \(-2\) \(1\) \(0\) \(-21\) $-$ $+$ $+$
4025.2.a.be $21$ $32.140$ None \(2\) \(-1\) \(0\) \(21\) $-$ $-$ $-$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4025))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4025)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(161))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(175))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(575))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(805))\)\(^{\oplus 2}\)