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Properties

Label 4425.2.a
Level $4425$
Weight $2$
Character orbit 4425.a
Rep. character $\chi_{4425}(1,\cdot)$
Character field $\Q$
Dimension $184$
Newform subspaces $42$
Sturm bound $1200$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 4425 = 3 \cdot 5^{2} \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4425.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 42 \)
Sturm bound: \(1200\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4425))\).

Total New Old
Modular forms 612 184 428
Cusp forms 589 184 405
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.

\(3\)\(5\)\(59\)FrickeDim
\(+\)\(+\)\(+\)$+$\(21\)
\(+\)\(+\)\(-\)$-$\(24\)
\(+\)\(-\)\(+\)$-$\(25\)
\(+\)\(-\)\(-\)$+$\(23\)
\(-\)\(+\)\(+\)$-$\(22\)
\(-\)\(+\)\(-\)$+$\(19\)
\(-\)\(-\)\(+\)$+$\(24\)
\(-\)\(-\)\(-\)$-$\(26\)
Plus space\(+\)\(87\)
Minus space\(-\)\(97\)

Trace form

\( 184 q - 2 q^{2} - 2 q^{3} + 184 q^{4} + 4 q^{6} - 4 q^{7} - 6 q^{8} + 184 q^{9} + O(q^{10}) \) \( 184 q - 2 q^{2} - 2 q^{3} + 184 q^{4} + 4 q^{6} - 4 q^{7} - 6 q^{8} + 184 q^{9} - 4 q^{11} - 6 q^{12} + 4 q^{13} - 4 q^{14} + 184 q^{16} + 20 q^{17} - 2 q^{18} + 8 q^{19} - 12 q^{21} + 4 q^{22} - 16 q^{26} - 2 q^{27} - 20 q^{28} - 40 q^{29} - 16 q^{31} - 14 q^{32} - 52 q^{34} + 184 q^{36} - 4 q^{37} - 28 q^{38} - 16 q^{39} - 8 q^{41} + 8 q^{42} - 16 q^{43} - 76 q^{44} - 12 q^{46} + 20 q^{47} - 14 q^{48} + 168 q^{49} + 12 q^{51} + 40 q^{52} + 4 q^{53} + 4 q^{54} - 52 q^{56} - 16 q^{57} - 32 q^{58} - 36 q^{61} + 24 q^{62} - 4 q^{63} + 148 q^{64} + 24 q^{66} + 16 q^{67} + 68 q^{68} + 20 q^{69} - 4 q^{71} - 6 q^{72} + 8 q^{73} - 28 q^{74} + 48 q^{76} + 28 q^{77} - 16 q^{78} - 40 q^{79} + 184 q^{81} + 40 q^{82} + 52 q^{83} - 16 q^{84} - 88 q^{86} - 8 q^{87} + 8 q^{89} - 36 q^{91} + 20 q^{92} - 4 q^{93} - 36 q^{96} - 36 q^{97} + 34 q^{98} - 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4425))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 5 59
4425.2.a.a 4425.a 1.a $1$ $35.334$ \(\Q\) None \(-2\) \(1\) \(0\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}-2q^{6}-2q^{7}+\cdots\)
4425.2.a.b 4425.a 1.a $1$ $35.334$ \(\Q\) None \(-2\) \(1\) \(0\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}-2q^{6}+q^{7}+q^{9}+\cdots\)
4425.2.a.c 4425.a 1.a $1$ $35.334$ \(\Q\) None \(-1\) \(-1\) \(0\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{6}-4q^{7}+3q^{8}+\cdots\)
4425.2.a.d 4425.a 1.a $1$ $35.334$ \(\Q\) None \(-1\) \(-1\) \(0\) \(-1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{6}-q^{7}+3q^{8}+\cdots\)
4425.2.a.e 4425.a 1.a $1$ $35.334$ \(\Q\) None \(-1\) \(1\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{6}+3q^{8}+q^{9}+\cdots\)
4425.2.a.f 4425.a 1.a $1$ $35.334$ \(\Q\) None \(-1\) \(1\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{6}+3q^{8}+q^{9}+\cdots\)
4425.2.a.g 4425.a 1.a $1$ $35.334$ \(\Q\) None \(-1\) \(1\) \(0\) \(5\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{6}+5q^{7}+3q^{8}+\cdots\)
4425.2.a.h 4425.a 1.a $1$ $35.334$ \(\Q\) None \(0\) \(-1\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}+q^{9}-5q^{11}+2q^{12}+\cdots\)
4425.2.a.i 4425.a 1.a $1$ $35.334$ \(\Q\) None \(1\) \(-1\) \(0\) \(-5\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{6}-5q^{7}-3q^{8}+\cdots\)
4425.2.a.j 4425.a 1.a $1$ $35.334$ \(\Q\) None \(1\) \(-1\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{6}-3q^{8}+q^{9}+\cdots\)
4425.2.a.k 4425.a 1.a $1$ $35.334$ \(\Q\) None \(1\) \(1\) \(0\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{6}+q^{7}-3q^{8}+\cdots\)
4425.2.a.l 4425.a 1.a $1$ $35.334$ \(\Q\) None \(1\) \(1\) \(0\) \(4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{6}+4q^{7}-3q^{8}+\cdots\)
4425.2.a.m 4425.a 1.a $1$ $35.334$ \(\Q\) None \(2\) \(-1\) \(0\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}-2q^{6}-q^{7}+q^{9}+\cdots\)
4425.2.a.n 4425.a 1.a $1$ $35.334$ \(\Q\) None \(2\) \(-1\) \(0\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}-2q^{6}+2q^{7}+\cdots\)
4425.2.a.o 4425.a 1.a $2$ $35.334$ \(\Q(\sqrt{5}) \) None \(-1\) \(-2\) \(0\) \(-1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots\)
4425.2.a.p 4425.a 1.a $2$ $35.334$ \(\Q(\sqrt{17}) \) None \(-1\) \(2\) \(0\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(2+\beta )q^{4}-\beta q^{6}+\beta q^{7}+\cdots\)
4425.2.a.q 4425.a 1.a $2$ $35.334$ \(\Q(\sqrt{2}) \) None \(0\) \(-2\) \(0\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}-\beta q^{6}+(2-\beta )q^{7}-2\beta q^{8}+\cdots\)
4425.2.a.r 4425.a 1.a $2$ $35.334$ \(\Q(\sqrt{6}) \) None \(0\) \(-2\) \(0\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+4q^{4}-\beta q^{6}+(-2+\beta )q^{7}+\cdots\)
4425.2.a.s 4425.a 1.a $2$ $35.334$ \(\Q(\sqrt{17}) \) None \(1\) \(-2\) \(0\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+(2+\beta )q^{4}-\beta q^{6}-\beta q^{7}+\cdots\)
4425.2.a.t 4425.a 1.a $2$ $35.334$ \(\Q(\sqrt{5}) \) None \(1\) \(2\) \(0\) \(7\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots\)
4425.2.a.u 4425.a 1.a $2$ $35.334$ \(\Q(\sqrt{5}) \) None \(3\) \(-2\) \(0\) \(7\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}-q^{3}+3\beta q^{4}+(-1-\beta )q^{6}+\cdots\)
4425.2.a.v 4425.a 1.a $3$ $35.334$ 3.3.316.1 None \(-2\) \(3\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+q^{3}+(2-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
4425.2.a.w 4425.a 1.a $3$ $35.334$ 3.3.229.1 None \(0\) \(3\) \(0\) \(-9\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
4425.2.a.x 4425.a 1.a $3$ $35.334$ 3.3.316.1 None \(1\) \(3\) \(0\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
4425.2.a.y 4425.a 1.a $4$ $35.334$ 4.4.11344.1 None \(-2\) \(4\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
4425.2.a.z 4425.a 1.a $4$ $35.334$ 4.4.19664.1 None \(-2\) \(4\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+q^{3}+(2+\beta _{2})q^{4}+\cdots\)
4425.2.a.ba 4425.a 1.a $4$ $35.334$ 4.4.1957.1 None \(-1\) \(-4\) \(0\) \(1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(\beta _{1}+\beta _{2})q^{2}-q^{3}-\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
4425.2.a.bb 4425.a 1.a $4$ $35.334$ 4.4.1957.1 None \(1\) \(4\) \(0\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}-\beta _{2})q^{2}+q^{3}-\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
4425.2.a.bc 4425.a 1.a $4$ $35.334$ 4.4.11344.1 None \(2\) \(-4\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
4425.2.a.bd 4425.a 1.a $6$ $35.334$ 6.6.21655296.1 None \(-2\) \(-6\) \(0\) \(-6\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{3}+\beta _{4})q^{4}+\beta _{1}q^{6}+\cdots\)
4425.2.a.be 4425.a 1.a $6$ $35.334$ 6.6.33824236.1 None \(-1\) \(6\) \(0\) \(-7\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
4425.2.a.bf 4425.a 1.a $6$ $35.334$ 6.6.33824236.1 None \(1\) \(-6\) \(0\) \(7\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
4425.2.a.bg 4425.a 1.a $6$ $35.334$ 6.6.22298624.1 None \(4\) \(6\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
4425.2.a.bh 4425.a 1.a $9$ $35.334$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(-3\) \(-9\) \(0\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
4425.2.a.bi 4425.a 1.a $10$ $35.334$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-5\) \(-10\) \(0\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}-q^{3}+(1+\beta _{2})q^{4}+\cdots\)
4425.2.a.bj 4425.a 1.a $10$ $35.334$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(5\) \(10\) \(0\) \(-3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+q^{3}+(1+\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots\)
4425.2.a.bk 4425.a 1.a $11$ $35.334$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-3\) \(-11\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
4425.2.a.bl 4425.a 1.a $11$ $35.334$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(3\) \(11\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
4425.2.a.bm 4425.a 1.a $13$ $35.334$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(-4\) \(13\) \(0\) \(-17\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
4425.2.a.bn 4425.a 1.a $13$ $35.334$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(-3\) \(-13\) \(0\) \(-10\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
4425.2.a.bo 4425.a 1.a $13$ $35.334$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(3\) \(13\) \(0\) \(10\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
4425.2.a.bp 4425.a 1.a $13$ $35.334$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(4\) \(-13\) \(0\) \(17\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4425))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(4425)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(59))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(177))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(295))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(885))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1475))\)\(^{\oplus 2}\)