Properties

Label 5225.2.a
Level $5225$
Weight $2$
Character orbit 5225.a
Rep. character $\chi_{5225}(1,\cdot)$
Character field $\Q$
Dimension $286$
Newform subspaces $29$
Sturm bound $1200$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 5225 = 5^{2} \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5225.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 29 \)
Sturm bound: \(1200\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5225))\).

Total New Old
Modular forms 612 286 326
Cusp forms 589 286 303
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.

\(5\)\(11\)\(19\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(32\)
\(+\)\(+\)\(-\)\(-\)\(37\)
\(+\)\(-\)\(+\)\(-\)\(35\)
\(+\)\(-\)\(-\)\(+\)\(30\)
\(-\)\(+\)\(+\)\(-\)\(41\)
\(-\)\(+\)\(-\)\(+\)\(31\)
\(-\)\(-\)\(+\)\(+\)\(35\)
\(-\)\(-\)\(-\)\(-\)\(45\)
Plus space\(+\)\(128\)
Minus space\(-\)\(158\)

Trace form

\( 286 q + 2 q^{2} + 2 q^{3} + 288 q^{4} - 4 q^{6} - 6 q^{8} + 300 q^{9} + O(q^{10}) \) \( 286 q + 2 q^{2} + 2 q^{3} + 288 q^{4} - 4 q^{6} - 6 q^{8} + 300 q^{9} + 4 q^{11} - 24 q^{12} + 16 q^{13} - 4 q^{14} + 300 q^{16} + 16 q^{17} - 22 q^{18} + 32 q^{21} - 10 q^{23} - 20 q^{24} - 20 q^{26} + 14 q^{27} + 32 q^{28} + 8 q^{29} + 14 q^{31} + 10 q^{32} + 2 q^{33} + 20 q^{34} + 360 q^{36} + 38 q^{37} - 6 q^{38} - 36 q^{39} - 4 q^{41} + 64 q^{42} - 20 q^{43} + 18 q^{44} + 48 q^{46} - 32 q^{47} + 28 q^{48} + 322 q^{49} - 32 q^{51} + 84 q^{52} + 36 q^{53} + 16 q^{54} + 44 q^{56} + 4 q^{58} - 2 q^{59} + 28 q^{61} + 28 q^{62} - 24 q^{63} + 268 q^{64} + 8 q^{66} - 14 q^{67} + 56 q^{68} + 42 q^{69} - 2 q^{71} - 30 q^{72} + 48 q^{73} - 44 q^{74} - 12 q^{77} + 84 q^{78} + 16 q^{79} + 334 q^{81} + 36 q^{82} - 48 q^{83} + 168 q^{84} + 24 q^{86} - 28 q^{87} + 30 q^{89} + 24 q^{91} - 28 q^{92} - 14 q^{93} - 72 q^{94} - 4 q^{96} + 50 q^{97} + 42 q^{98} - 18 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5225))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5 11 19
5225.2.a.a 5225.a 1.a $1$ $41.722$ \(\Q\) None 1045.2.a.b \(-1\) \(0\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+3q^{8}-3q^{9}-q^{11}-2q^{13}+\cdots\)
5225.2.a.b 5225.a 1.a $1$ $41.722$ \(\Q\) None 209.2.a.a \(0\) \(-1\) \(0\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}+4q^{7}-2q^{9}+q^{11}+\cdots\)
5225.2.a.c 5225.a 1.a $1$ $41.722$ \(\Q\) None 1045.2.a.a \(1\) \(2\) \(0\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}-q^{4}+2q^{6}+2q^{7}-3q^{8}+\cdots\)
5225.2.a.d 5225.a 1.a $2$ $41.722$ \(\Q(\sqrt{2}) \) None 1045.2.b.a \(-2\) \(-4\) \(0\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}-2q^{3}+(1-2\beta )q^{4}+\cdots\)
5225.2.a.e 5225.a 1.a $2$ $41.722$ \(\Q(\sqrt{2}) \) None 1045.2.a.c \(-2\) \(-4\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}-2q^{3}+(1-2\beta )q^{4}+\cdots\)
5225.2.a.f 5225.a 1.a $2$ $41.722$ \(\Q(\sqrt{2}) \) None 209.2.a.b \(0\) \(2\) \(0\) \(4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1-\beta )q^{3}+(-2+\beta )q^{6}+(2+\cdots)q^{7}+\cdots\)
5225.2.a.g 5225.a 1.a $2$ $41.722$ \(\Q(\sqrt{2}) \) None 1045.2.b.a \(2\) \(4\) \(0\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+2q^{3}+(1+2\beta )q^{4}+(2+\cdots)q^{6}+\cdots\)
5225.2.a.h 5225.a 1.a $5$ $41.722$ 5.5.246832.1 None 209.2.a.c \(-2\) \(-1\) \(0\) \(-6\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}-\beta _{3}q^{3}+(\beta _{1}+\beta _{2}+\beta _{3}+\beta _{4})q^{4}+\cdots\)
5225.2.a.i 5225.a 1.a $5$ $41.722$ 5.5.36497.1 None 1045.2.a.e \(1\) \(3\) \(0\) \(-3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{4}q^{2}+(1-\beta _{1})q^{3}+\beta _{3}q^{4}+(-1+\cdots)q^{6}+\cdots\)
5225.2.a.j 5225.a 1.a $5$ $41.722$ \(\Q(\zeta_{22})^+\) None 1045.2.a.d \(3\) \(7\) \(0\) \(11\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(\beta _{1}+\beta _{3}-\beta _{4})q^{2}+(2-\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
5225.2.a.k 5225.a 1.a $6$ $41.722$ 6.6.131947641.1 None 1045.2.a.g \(0\) \(-3\) \(0\) \(-5\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1+\beta _{3})q^{3}+(2+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
5225.2.a.l 5225.a 1.a $6$ $41.722$ 6.6.7281497.1 None 1045.2.a.f \(2\) \(1\) \(0\) \(-5\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{4}q^{2}-\beta _{3}q^{3}+(\beta _{4}+\beta _{5})q^{4}+\beta _{2}q^{6}+\cdots\)
5225.2.a.m 5225.a 1.a $7$ $41.722$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 1045.2.a.h \(-1\) \(-3\) \(0\) \(1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{5}q^{3}+(1+\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{6}+\cdots\)
5225.2.a.n 5225.a 1.a $7$ $41.722$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 209.2.a.d \(1\) \(-2\) \(0\) \(-10\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(2+\beta _{2}+\beta _{3})q^{4}+\cdots\)
5225.2.a.o 5225.a 1.a $8$ $41.722$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 1045.2.a.i \(6\) \(7\) \(0\) \(11\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1+\beta _{6})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots\)
5225.2.a.p 5225.a 1.a $9$ $41.722$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 1045.2.a.k \(-3\) \(-3\) \(0\) \(-13\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{5}q^{3}+(1+\beta _{2})q^{4}-\beta _{8}q^{6}+\cdots\)
5225.2.a.q 5225.a 1.a $9$ $41.722$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None 1045.2.a.j \(-3\) \(-3\) \(0\) \(9\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(1-\beta _{1}-\beta _{8})q^{4}+\cdots\)
5225.2.a.r 5225.a 1.a $15$ $41.722$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None 5225.2.a.r \(-5\) \(-4\) \(0\) \(-21\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{5}q^{3}+(1+\beta _{2})q^{4}+(-\beta _{4}+\cdots)q^{6}+\cdots\)
5225.2.a.s 5225.a 1.a $15$ $41.722$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None 5225.2.a.s \(-5\) \(-4\) \(0\) \(-15\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
5225.2.a.t 5225.a 1.a $15$ $41.722$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None 5225.2.a.t \(-1\) \(4\) \(0\) \(11\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{8}q^{3}+(1+\beta _{2})q^{4}+(-\beta _{11}+\cdots)q^{6}+\cdots\)
5225.2.a.u 5225.a 1.a $15$ $41.722$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None 5225.2.a.u \(-1\) \(4\) \(0\) \(17\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{7}q^{3}+(1+\beta _{2})q^{4}+\beta _{4}q^{6}+\cdots\)
5225.2.a.v 5225.a 1.a $15$ $41.722$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None 5225.2.a.u \(1\) \(-4\) \(0\) \(-17\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{7}q^{3}+(1+\beta _{2})q^{4}+\beta _{4}q^{6}+\cdots\)
5225.2.a.w 5225.a 1.a $15$ $41.722$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None 5225.2.a.t \(1\) \(-4\) \(0\) \(-11\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{8}q^{3}+(1+\beta _{2})q^{4}+(-\beta _{11}+\cdots)q^{6}+\cdots\)
5225.2.a.x 5225.a 1.a $15$ $41.722$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None 5225.2.a.s \(5\) \(4\) \(0\) \(15\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
5225.2.a.y 5225.a 1.a $15$ $41.722$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None 5225.2.a.r \(5\) \(4\) \(0\) \(21\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(1+\beta _{2})q^{4}+(-\beta _{4}+\cdots)q^{6}+\cdots\)
5225.2.a.z 5225.a 1.a $16$ $41.722$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 1045.2.b.b \(0\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{11}q^{3}+\beta _{2}q^{4}+(-1+\beta _{6}+\cdots)q^{6}+\cdots\)
5225.2.a.ba 5225.a 1.a $20$ $41.722$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None 1045.2.b.c \(0\) \(0\) \(0\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{6}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{6}+\cdots\)
5225.2.a.bb 5225.a 1.a $22$ $41.722$ None 1045.2.b.d \(0\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$
5225.2.a.bc 5225.a 1.a $30$ $41.722$ None 1045.2.b.e \(0\) \(0\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5225))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5225)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(95))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(209))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(275))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(475))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1045))\)\(^{\oplus 2}\)