↑

Properties

Label 5525.2.a
Level $5525$
Weight $2$
Character orbit 5525.a
Rep. character $\chi_{5525}(1,\cdot)$
Character field $\Q$
Dimension $304$
Newform subspaces $45$
Sturm bound $1260$
Trace bound $11$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 5525 = 5^{2} \cdot 13 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5525.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 45 \)
Sturm bound: \(1260\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(3\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5525))\).

Total New Old
Modular forms 640 304 336
Cusp forms 617 304 313
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.

\(5\)\(13\)\(17\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(34\)
\(+\)\(+\)\(-\)\(-\)\(38\)
\(+\)\(-\)\(+\)\(-\)\(38\)
\(+\)\(-\)\(-\)\(+\)\(34\)
\(-\)\(+\)\(+\)\(-\)\(44\)
\(-\)\(+\)\(-\)\(+\)\(36\)
\(-\)\(-\)\(+\)\(+\)\(36\)
\(-\)\(-\)\(-\)\(-\)\(44\)
Plus space\(+\)\(140\)
Minus space\(-\)\(164\)

Trace form

\( 304 q - 4 q^{2} + 4 q^{3} + 300 q^{4} + 12 q^{6} + 4 q^{7} + 316 q^{9} + O(q^{10}) \) \( 304 q - 4 q^{2} + 4 q^{3} + 300 q^{4} + 12 q^{6} + 4 q^{7} + 316 q^{9} + 24 q^{12} + 16 q^{14} + 284 q^{16} + 8 q^{18} + 32 q^{21} - 8 q^{22} + 64 q^{24} + 28 q^{27} + 8 q^{28} + 12 q^{29} + 32 q^{31} + 16 q^{32} + 28 q^{33} + 4 q^{34} + 324 q^{36} - 8 q^{37} + 20 q^{38} + 8 q^{39} + 12 q^{41} - 4 q^{42} + 16 q^{43} - 96 q^{44} - 48 q^{46} + 48 q^{47} + 20 q^{48} + 348 q^{49} + 8 q^{52} + 12 q^{53} + 60 q^{54} + 24 q^{56} + 4 q^{57} - 12 q^{58} - 20 q^{59} + 4 q^{61} - 44 q^{62} - 8 q^{63} + 248 q^{64} + 100 q^{66} - 24 q^{67} - 28 q^{71} + 32 q^{72} - 16 q^{73} + 20 q^{74} + 84 q^{76} - 8 q^{77} - 24 q^{78} - 20 q^{79} + 360 q^{81} + 44 q^{82} - 12 q^{83} + 116 q^{84} - 56 q^{86} + 36 q^{87} - 28 q^{88} - 16 q^{89} + 8 q^{91} - 40 q^{92} + 52 q^{93} + 72 q^{94} + 196 q^{96} + 60 q^{97} - 88 q^{98} - 64 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5525))\) 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 13 17
5525.2.a.a 5525.a 1.a $1$ $44.117$ \(\Q\) None 5525.2.a.a \(-2\) \(-1\) \(0\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}+2q^{6}-2q^{7}+\cdots\)
5525.2.a.b 5525.a 1.a $1$ $44.117$ \(\Q\) None 5525.2.a.b \(-2\) \(3\) \(0\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+2q^{4}-6q^{6}+2q^{7}+\cdots\)
5525.2.a.c 5525.a 1.a $1$ $44.117$ \(\Q\) None 221.2.a.b \(-1\) \(-2\) \(0\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}-q^{4}+2q^{6}-2q^{7}+3q^{8}+\cdots\)
5525.2.a.d 5525.a 1.a $1$ $44.117$ \(\Q\) None 5525.2.a.d \(0\) \(-3\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-2q^{4}+6q^{9}+6q^{12}+q^{13}+\cdots\)
5525.2.a.e 5525.a 1.a $1$ $44.117$ \(\Q\) None 5525.2.a.e \(0\) \(-1\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}-2q^{7}-2q^{9}+2q^{11}+\cdots\)
5525.2.a.f 5525.a 1.a $1$ $44.117$ \(\Q\) None 5525.2.a.e \(0\) \(1\) \(0\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}+2q^{7}-2q^{9}+2q^{11}+\cdots\)
5525.2.a.g 5525.a 1.a $1$ $44.117$ \(\Q\) None 5525.2.a.d \(0\) \(3\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+3q^{3}-2q^{4}+6q^{9}-6q^{12}-q^{13}+\cdots\)
5525.2.a.h 5525.a 1.a $1$ $44.117$ \(\Q\) None 1105.2.a.a \(1\) \(0\) \(0\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+2q^{7}-3q^{8}-3q^{9}-4q^{11}+\cdots\)
5525.2.a.i 5525.a 1.a $1$ $44.117$ \(\Q\) None 221.2.a.a \(1\) \(0\) \(0\) \(2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+2q^{7}-3q^{8}-3q^{9}+6q^{11}+\cdots\)
5525.2.a.j 5525.a 1.a $1$ $44.117$ \(\Q\) None 5525.2.a.b \(2\) \(-3\) \(0\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+2q^{4}-6q^{6}-2q^{7}+\cdots\)
5525.2.a.k 5525.a 1.a $1$ $44.117$ \(\Q\) None 5525.2.a.a \(2\) \(1\) \(0\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}+2q^{6}+2q^{7}+\cdots\)
5525.2.a.l 5525.a 1.a $2$ $44.117$ \(\Q(\sqrt{5}) \) None 5525.2.a.l \(-4\) \(2\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}-2q^{6}-\beta q^{7}+\cdots\)
5525.2.a.m 5525.a 1.a $2$ $44.117$ \(\Q(\sqrt{5}) \) None 1105.2.a.d \(-2\) \(-2\) \(0\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta )q^{3}-q^{4}+(1-\beta )q^{6}+\cdots\)
5525.2.a.n 5525.a 1.a $2$ $44.117$ \(\Q(\sqrt{5}) \) None 1105.2.a.c \(-2\) \(4\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}-q^{4}-2q^{6}-\beta q^{7}+3q^{8}+\cdots\)
5525.2.a.o 5525.a 1.a $2$ $44.117$ \(\Q(\sqrt{5}) \) None 221.2.a.e \(0\) \(-2\) \(0\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-1+\beta )q^{3}+3q^{4}+(-5+\cdots)q^{6}+\cdots\)
5525.2.a.p 5525.a 1.a $2$ $44.117$ \(\Q(\sqrt{21}) \) None 221.2.a.d \(1\) \(-1\) \(0\) \(5\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1+\beta )q^{3}+(3+\beta )q^{4}+5q^{6}+\cdots\)
5525.2.a.q 5525.a 1.a $2$ $44.117$ \(\Q(\sqrt{5}) \) None 221.2.a.c \(1\) \(3\) \(0\) \(1\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1+\beta )q^{3}+(-1+\beta )q^{4}+(1+\cdots)q^{6}+\cdots\)
5525.2.a.r 5525.a 1.a $2$ $44.117$ \(\Q(\sqrt{2}) \) None 1105.2.a.b \(2\) \(0\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}-q^{4}+\beta q^{6}-\beta q^{7}-3q^{8}+\cdots\)
5525.2.a.s 5525.a 1.a $2$ $44.117$ \(\Q(\sqrt{5}) \) None 5525.2.a.l \(4\) \(-2\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-q^{3}+2q^{4}-2q^{6}+\beta q^{7}+\cdots\)
5525.2.a.t 5525.a 1.a $3$ $44.117$ 3.3.148.1 None 1105.2.b.a \(-3\) \(6\) \(0\) \(8\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+2q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
5525.2.a.u 5525.a 1.a $3$ $44.117$ 3.3.148.1 None 1105.2.b.b \(-1\) \(0\) \(0\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots\)
5525.2.a.v 5525.a 1.a $3$ $44.117$ 3.3.229.1 None 221.2.a.f \(0\) \(3\) \(0\) \(9\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1-\beta _{1})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
5525.2.a.w 5525.a 1.a $3$ $44.117$ 3.3.148.1 None 1105.2.b.b \(1\) \(0\) \(0\) \(4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots\)
5525.2.a.x 5525.a 1.a $3$ $44.117$ 3.3.148.1 None 1105.2.b.a \(3\) \(-6\) \(0\) \(-8\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{2}-2q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
5525.2.a.y 5525.a 1.a $5$ $44.117$ 5.5.36497.1 None 1105.2.a.e \(2\) \(1\) \(0\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots\)
5525.2.a.z 5525.a 1.a $6$ $44.117$ 6.6.3697873.1 None 1105.2.a.g \(-3\) \(-3\) \(0\) \(-8\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1}-\beta _{5})q^{2}+(-1+\beta _{3})q^{3}+\cdots\)
5525.2.a.ba 5525.a 1.a $6$ $44.117$ 6.6.47150057.1 None 1105.2.a.f \(-3\) \(1\) \(0\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}-\beta _{5})q^{2}-\beta _{4}q^{3}+(2+\beta _{1}+\cdots)q^{4}+\cdots\)
5525.2.a.bb 5525.a 1.a $6$ $44.117$ 6.6.28134208.1 None 221.2.a.g \(-1\) \(-1\) \(0\) \(-7\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{4}q^{2}-\beta _{1}q^{3}+(1-\beta _{3})q^{4}-\beta _{2}q^{6}+\cdots\)
5525.2.a.bc 5525.a 1.a $7$ $44.117$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 1105.2.a.h \(4\) \(3\) \(0\) \(10\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}-\beta _{5}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
5525.2.a.bd 5525.a 1.a $8$ $44.117$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 1105.2.a.l \(-5\) \(-3\) \(0\) \(-12\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+\beta _{6}q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
5525.2.a.be 5525.a 1.a $8$ $44.117$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 1105.2.a.k \(-3\) \(-1\) \(0\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(1+\beta _{1}+\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
5525.2.a.bf 5525.a 1.a $8$ $44.117$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 1105.2.a.j \(1\) \(-5\) \(0\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(1+\beta _{1}-\beta _{3}+\cdots)q^{4}+\cdots\)
5525.2.a.bg 5525.a 1.a $8$ $44.117$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 1105.2.a.i \(3\) \(9\) \(0\) \(12\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}+(1+\beta _{1})q^{3}+(1+\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots\)
5525.2.a.bh 5525.a 1.a $13$ $44.117$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None 5525.2.a.bh \(-1\) \(-7\) \(0\) \(-9\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
5525.2.a.bi 5525.a 1.a $13$ $44.117$ \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None 5525.2.a.bh \(1\) \(7\) \(0\) \(9\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{4})q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
5525.2.a.bj 5525.a 1.a $15$ $44.117$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None 5525.2.a.bj \(-3\) \(-9\) \(0\) \(-15\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1-\beta _{11})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
5525.2.a.bk 5525.a 1.a $15$ $44.117$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None 5525.2.a.bk \(-3\) \(-7\) \(0\) \(-7\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{6}q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
5525.2.a.bl 5525.a 1.a $15$ $44.117$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None 5525.2.a.bl \(-1\) \(-5\) \(0\) \(-15\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
5525.2.a.bm 5525.a 1.a $15$ $44.117$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None 5525.2.a.bl \(1\) \(5\) \(0\) \(15\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
5525.2.a.bn 5525.a 1.a $15$ $44.117$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None 5525.2.a.bk \(3\) \(7\) \(0\) \(7\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
5525.2.a.bo 5525.a 1.a $15$ $44.117$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None 5525.2.a.bj \(3\) \(9\) \(0\) \(15\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{11})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
5525.2.a.bp 5525.a 1.a $17$ $44.117$ \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None 1105.2.b.c \(-1\) \(4\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+\beta _{8}q^{3}+(1+\beta _{2})q^{4}+(-\beta _{13}+\cdots)q^{6}+\cdots\)
5525.2.a.bq 5525.a 1.a $17$ $44.117$ \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None 1105.2.b.c \(1\) \(-4\) \(0\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{8}q^{3}+(1+\beta _{2})q^{4}+(-\beta _{13}+\cdots)q^{6}+\cdots\)
5525.2.a.br 5525.a 1.a $25$ $44.117$ None 1105.2.b.d \(-5\) \(2\) \(0\) \(-6\) $-$ $+$ $+$ $\mathrm{SU}(2)$
5525.2.a.bs 5525.a 1.a $25$ $44.117$ None 1105.2.b.d \(5\) \(-2\) \(0\) \(6\) $-$ $-$ $-$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5525))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5525)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(85))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(221))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(325))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(425))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1105))\)\(^{\oplus 2}\)