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Properties

Label 1725.2.a
Level $1725$
Weight $2$
Character orbit 1725.a
Rep. character $\chi_{1725}(1,\cdot)$
Character field $\Q$
Dimension $70$
Newform subspaces $38$
Sturm bound $480$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 1725 = 3 \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1725.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 38 \)
Sturm bound: \(480\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(1725))\).

Total New Old
Modular forms 252 70 182
Cusp forms 229 70 159
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.

\(3\)\(5\)\(23\)FrickeDim
\(+\)\(+\)\(+\)$+$\(8\)
\(+\)\(+\)\(-\)$-$\(10\)
\(+\)\(-\)\(+\)$-$\(11\)
\(+\)\(-\)\(-\)$+$\(7\)
\(-\)\(+\)\(+\)$-$\(8\)
\(-\)\(+\)\(-\)$+$\(6\)
\(-\)\(-\)\(+\)$+$\(8\)
\(-\)\(-\)\(-\)$-$\(12\)
Plus space\(+\)\(29\)
Minus space\(-\)\(41\)

Trace form

\( 70 q + 2 q^{2} - 2 q^{3} + 70 q^{4} + 2 q^{6} + 18 q^{8} + 70 q^{9} + O(q^{10}) \) \( 70 q + 2 q^{2} - 2 q^{3} + 70 q^{4} + 2 q^{6} + 18 q^{8} + 70 q^{9} + 2 q^{12} - 4 q^{13} + 20 q^{14} + 94 q^{16} + 8 q^{17} + 2 q^{18} - 12 q^{19} - 16 q^{21} - 8 q^{22} - 6 q^{24} - 12 q^{26} - 2 q^{27} - 28 q^{29} + 4 q^{31} + 18 q^{32} + 8 q^{33} - 44 q^{34} + 70 q^{36} + 4 q^{37} + 12 q^{38} - 8 q^{39} - 4 q^{41} - 8 q^{42} + 24 q^{44} + 4 q^{46} + 32 q^{47} + 2 q^{48} + 50 q^{49} - 4 q^{51} - 36 q^{52} + 2 q^{54} + 20 q^{56} - 12 q^{57} + 44 q^{58} + 32 q^{59} - 64 q^{61} - 56 q^{62} + 166 q^{64} + 32 q^{66} + 24 q^{67} + 56 q^{68} + 4 q^{69} + 72 q^{71} + 18 q^{72} + 36 q^{73} + 4 q^{74} - 56 q^{76} - 40 q^{77} - 4 q^{78} - 40 q^{79} + 70 q^{81} - 20 q^{82} - 16 q^{83} - 28 q^{84} + 4 q^{86} - 20 q^{87} + 16 q^{88} - 8 q^{89} - 52 q^{91} - 24 q^{93} + 56 q^{94} - 30 q^{96} + 4 q^{97} + 74 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(1725))\) 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 23
1725.2.a.a 1725.a 1.a $1$ $13.774$ \(\Q\) None \(-2\) \(1\) \(0\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}-2q^{6}-3q^{7}+\cdots\)
1725.2.a.b 1725.a 1.a $1$ $13.774$ \(\Q\) None \(-1\) \(-1\) \(0\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{6}-4q^{7}+3q^{8}+\cdots\)
1725.2.a.c 1725.a 1.a $1$ $13.774$ \(\Q\) None \(-1\) \(-1\) \(0\) \(-3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{6}-3q^{7}+3q^{8}+\cdots\)
1725.2.a.d 1725.a 1.a $1$ $13.774$ \(\Q\) None \(-1\) \(-1\) \(0\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{6}-2q^{7}+3q^{8}+\cdots\)
1725.2.a.e 1725.a 1.a $1$ $13.774$ \(\Q\) None \(-1\) \(-1\) \(0\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{6}+2q^{7}+3q^{8}+\cdots\)
1725.2.a.f 1725.a 1.a $1$ $13.774$ \(\Q\) None \(-1\) \(-1\) \(0\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}-q^{4}+q^{6}+3q^{7}+3q^{8}+\cdots\)
1725.2.a.g 1725.a 1.a $1$ $13.774$ \(\Q\) None \(-1\) \(1\) \(0\) \(-5\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{6}-5q^{7}+3q^{8}+\cdots\)
1725.2.a.h 1725.a 1.a $1$ $13.774$ \(\Q\) None \(-1\) \(1\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{6}+3q^{8}+q^{9}+\cdots\)
1725.2.a.i 1725.a 1.a $1$ $13.774$ \(\Q\) None \(0\) \(-1\) \(0\) \(-3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}-3q^{7}+q^{9}+2q^{11}+\cdots\)
1725.2.a.j 1725.a 1.a $1$ $13.774$ \(\Q\) None \(0\) \(-1\) \(0\) \(1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}+q^{7}+q^{9}-6q^{11}+2q^{12}+\cdots\)
1725.2.a.k 1725.a 1.a $1$ $13.774$ \(\Q\) None \(0\) \(-1\) \(0\) \(3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}+3q^{7}+q^{9}-4q^{11}+\cdots\)
1725.2.a.l 1725.a 1.a $1$ $13.774$ \(\Q\) None \(0\) \(1\) \(0\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-q^{7}+q^{9}-6q^{11}-2q^{12}+\cdots\)
1725.2.a.m 1725.a 1.a $1$ $13.774$ \(\Q\) None \(0\) \(1\) \(0\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-q^{7}+q^{9}+4q^{11}-2q^{12}+\cdots\)
1725.2.a.n 1725.a 1.a $1$ $13.774$ \(\Q\) None \(0\) \(1\) \(0\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}+3q^{7}+q^{9}+2q^{11}+\cdots\)
1725.2.a.o 1725.a 1.a $1$ $13.774$ \(\Q\) None \(1\) \(-1\) \(0\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{6}-4q^{7}-3q^{8}+\cdots\)
1725.2.a.p 1725.a 1.a $1$ $13.774$ \(\Q\) None \(1\) \(-1\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{6}-3q^{8}+q^{9}+\cdots\)
1725.2.a.q 1725.a 1.a $1$ $13.774$ \(\Q\) None \(1\) \(-1\) \(0\) \(5\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{6}+5q^{7}-3q^{8}+\cdots\)
1725.2.a.r 1725.a 1.a $1$ $13.774$ \(\Q\) None \(1\) \(1\) \(0\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{6}-3q^{7}-3q^{8}+\cdots\)
1725.2.a.s 1725.a 1.a $1$ $13.774$ \(\Q\) None \(1\) \(1\) \(0\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{6}+2q^{7}-3q^{8}+\cdots\)
1725.2.a.t 1725.a 1.a $1$ $13.774$ \(\Q\) None \(1\) \(1\) \(0\) \(3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{6}+3q^{7}-3q^{8}+\cdots\)
1725.2.a.u 1725.a 1.a $1$ $13.774$ \(\Q\) None \(2\) \(-1\) \(0\) \(5\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}-2q^{6}+5q^{7}+\cdots\)
1725.2.a.v 1725.a 1.a $2$ $13.774$ \(\Q(\sqrt{5}) \) None \(-3\) \(2\) \(0\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}+q^{3}+3\beta q^{4}+(-1+\cdots)q^{6}+\cdots\)
1725.2.a.w 1725.a 1.a $2$ $13.774$ \(\Q(\sqrt{13}) \) None \(-1\) \(-2\) \(0\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}-q^{3}+(1+\beta )q^{4}+\beta q^{6}+(1+\cdots)q^{7}+\cdots\)
1725.2.a.x 1725.a 1.a $2$ $13.774$ \(\Q(\sqrt{21}) \) None \(-1\) \(2\) \(0\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(3+\beta )q^{4}-\beta q^{6}+(-1+\cdots)q^{7}+\cdots\)
1725.2.a.y 1725.a 1.a $2$ $13.774$ \(\Q(\sqrt{6}) \) None \(0\) \(-2\) \(0\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+4q^{4}-\beta q^{6}+q^{7}+2\beta q^{8}+\cdots\)
1725.2.a.z 1725.a 1.a $2$ $13.774$ \(\Q(\sqrt{2}) \) None \(0\) \(2\) \(0\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+\beta q^{6}+(1-2\beta )q^{7}-2\beta q^{8}+\cdots\)
1725.2.a.ba 1725.a 1.a $2$ $13.774$ \(\Q(\sqrt{5}) \) None \(0\) \(2\) \(0\) \(-2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+3q^{4}-\beta q^{6}+(-1+\beta )q^{7}+\cdots\)
1725.2.a.bb 1725.a 1.a $2$ $13.774$ \(\Q(\sqrt{21}) \) None \(1\) \(-2\) \(0\) \(1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+(3+\beta )q^{4}-\beta q^{6}+(1+\cdots)q^{7}+\cdots\)
1725.2.a.bc 1725.a 1.a $2$ $13.774$ \(\Q(\sqrt{13}) \) None \(1\) \(2\) \(0\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+(1+\beta )q^{4}+\beta q^{6}+(-1+\cdots)q^{7}+\cdots\)
1725.2.a.bd 1725.a 1.a $2$ $13.774$ \(\Q(\sqrt{3}) \) None \(2\) \(2\) \(0\) \(6\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+q^{3}+(2+2\beta )q^{4}+(1+\beta )q^{6}+\cdots\)
1725.2.a.be 1725.a 1.a $2$ $13.774$ \(\Q(\sqrt{5}) \) None \(3\) \(-2\) \(0\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}-q^{3}+3\beta q^{4}+(-1-\beta )q^{6}+\cdots\)
1725.2.a.bf 1725.a 1.a $3$ $13.774$ 3.3.229.1 None \(-2\) \(-3\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}-q^{3}+(2+\beta _{1})q^{4}+\cdots\)
1725.2.a.bg 1725.a 1.a $3$ $13.774$ 3.3.148.1 None \(0\) \(-3\) \(0\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}-q^{3}+(1-\beta _{1}-\beta _{2})q^{4}+\beta _{2}q^{6}+\cdots\)
1725.2.a.bh 1725.a 1.a $3$ $13.774$ 3.3.148.1 None \(0\) \(3\) \(0\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+q^{3}+(1-\beta _{1}-\beta _{2})q^{4}+\beta _{2}q^{6}+\cdots\)
1725.2.a.bi 1725.a 1.a $3$ $13.774$ 3.3.316.1 None \(1\) \(-3\) \(0\) \(-6\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
1725.2.a.bj 1725.a 1.a $3$ $13.774$ 3.3.229.1 None \(2\) \(3\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{2}+q^{3}+(2+\beta _{1})q^{4}+(1+\cdots)q^{6}+\cdots\)
1725.2.a.bk 1725.a 1.a $7$ $13.774$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-2\) \(-7\) \(0\) \(5\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}-q^{3}+(2-\beta _{3})q^{4}+\beta _{2}q^{6}+\cdots\)
1725.2.a.bl 1725.a 1.a $7$ $13.774$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(2\) \(7\) \(0\) \(-5\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+q^{3}+(2-\beta _{3})q^{4}+\beta _{2}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(1725))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(1725)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(345))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(575))\)\(^{\oplus 2}\)