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Properties

Label 5025.2.a
Level $5025$
Weight $2$
Character orbit 5025.a
Rep. character $\chi_{5025}(1,\cdot)$
Character field $\Q$
Dimension $210$
Newform subspaces $39$
Sturm bound $1360$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 5025 = 3 \cdot 5^{2} \cdot 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5025.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 39 \)
Sturm bound: \(1360\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(7\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5025))\).

Total New Old
Modular forms 692 210 482
Cusp forms 669 210 459
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.

\(3\)\(5\)\(67\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(26\)
\(+\)\(+\)\(-\)\(-\)\(23\)
\(+\)\(-\)\(+\)\(-\)\(29\)
\(+\)\(-\)\(-\)\(+\)\(27\)
\(-\)\(+\)\(+\)\(-\)\(29\)
\(-\)\(+\)\(-\)\(+\)\(20\)
\(-\)\(-\)\(+\)\(+\)\(23\)
\(-\)\(-\)\(-\)\(-\)\(33\)
Plus space\(+\)\(96\)
Minus space\(-\)\(114\)

Trace form

\( 210 q + 2 q^{2} + 216 q^{4} + 6 q^{6} + 8 q^{7} + 6 q^{8} + 210 q^{9} + O(q^{10}) \) \( 210 q + 2 q^{2} + 216 q^{4} + 6 q^{6} + 8 q^{7} + 6 q^{8} + 210 q^{9} + 12 q^{11} + 8 q^{12} + 8 q^{13} + 24 q^{14} + 252 q^{16} + 18 q^{17} + 2 q^{18} + 22 q^{19} + 4 q^{21} + 16 q^{22} + 14 q^{23} + 18 q^{24} - 32 q^{26} + 8 q^{28} - 18 q^{29} - 26 q^{32} + 4 q^{33} - 32 q^{34} + 216 q^{36} - 2 q^{37} - 28 q^{38} + 8 q^{39} - 4 q^{41} + 16 q^{42} + 20 q^{43} + 64 q^{44} - 10 q^{47} + 250 q^{49} + 4 q^{51} + 48 q^{52} + 32 q^{53} + 6 q^{54} + 60 q^{56} + 8 q^{57} - 8 q^{58} + 50 q^{59} - 12 q^{61} - 20 q^{62} + 8 q^{63} + 324 q^{64} + 16 q^{66} - 4 q^{67} + 24 q^{68} + 8 q^{69} + 6 q^{72} + 34 q^{73} - 40 q^{74} + 20 q^{76} + 4 q^{77} - 20 q^{78} + 16 q^{79} + 210 q^{81} - 64 q^{82} - 24 q^{83} + 12 q^{84} - 44 q^{86} + 12 q^{87} - 32 q^{88} - 30 q^{89} + 48 q^{91} + 76 q^{92} + 28 q^{93} - 16 q^{94} - 18 q^{96} - 6 q^{98} + 12 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5025))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 5 67
5025.2.a.a 5025.a 1.a $1$ $40.125$ \(\Q\) None 1005.2.c.a \(-1\) \(1\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{6}+3q^{8}+q^{9}+\cdots\)
5025.2.a.b 5025.a 1.a $1$ $40.125$ \(\Q\) None 1005.2.a.b \(-1\) \(1\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{6}+3q^{8}+q^{9}+\cdots\)
5025.2.a.c 5025.a 1.a $1$ $40.125$ \(\Q\) None 201.2.a.c \(-1\) \(1\) \(0\) \(3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{6}+3q^{7}+3q^{8}+\cdots\)
5025.2.a.d 5025.a 1.a $1$ $40.125$ \(\Q\) None 1005.2.a.a \(0\) \(-1\) \(0\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}-2q^{7}+q^{9}-6q^{11}+\cdots\)
5025.2.a.e 5025.a 1.a $1$ $40.125$ \(\Q\) None 5025.2.a.e \(0\) \(-1\) \(0\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}+2q^{7}+q^{9}+2q^{11}+\cdots\)
5025.2.a.f 5025.a 1.a $1$ $40.125$ \(\Q\) None 5025.2.a.e \(0\) \(1\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-2q^{7}+q^{9}+2q^{11}+\cdots\)
5025.2.a.g 5025.a 1.a $1$ $40.125$ \(\Q\) None 1005.2.c.a \(1\) \(-1\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{6}-3q^{8}+q^{9}+\cdots\)
5025.2.a.h 5025.a 1.a $1$ $40.125$ \(\Q\) None 201.2.a.b \(1\) \(-1\) \(0\) \(5\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{6}+5q^{7}-3q^{8}+\cdots\)
5025.2.a.i 5025.a 1.a $1$ $40.125$ \(\Q\) None 201.2.a.a \(2\) \(1\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}+2q^{6}+q^{9}-6q^{11}+\cdots\)
5025.2.a.j 5025.a 1.a $2$ $40.125$ \(\Q(\sqrt{6}) \) None 1005.2.c.b \(0\) \(-2\) \(0\) \(0\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{3}+4q^{4}-\beta q^{6}+\beta q^{7}+\cdots\)
5025.2.a.k 5025.a 1.a $2$ $40.125$ \(\Q(\sqrt{6}) \) None 1005.2.c.b \(0\) \(2\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+4q^{4}+\beta q^{6}+\beta q^{7}+\cdots\)
5025.2.a.l 5025.a 1.a $3$ $40.125$ 3.3.1620.1 None 5025.2.a.l \(-3\) \(3\) \(0\) \(-6\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{6}+(-2+\beta _{1}+\cdots)q^{7}+\cdots\)
5025.2.a.m 5025.a 1.a $3$ $40.125$ 3.3.148.1 None 201.2.a.d \(-3\) \(3\) \(0\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
5025.2.a.n 5025.a 1.a $3$ $40.125$ 3.3.568.1 None 5025.2.a.n \(-2\) \(-3\) \(0\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}-q^{3}+(3+\beta _{2})q^{4}+\cdots\)
5025.2.a.o 5025.a 1.a $3$ $40.125$ 3.3.148.1 None 5025.2.a.o \(-1\) \(-3\) \(0\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-\beta _{1}-\beta _{2})q^{2}-q^{3}+(1+2\beta _{1})q^{4}+\cdots\)
5025.2.a.p 5025.a 1.a $3$ $40.125$ 3.3.148.1 None 5025.2.a.o \(1\) \(3\) \(0\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(\beta _{1}+\beta _{2})q^{2}+q^{3}+(1+2\beta _{1})q^{4}+\cdots\)
5025.2.a.q 5025.a 1.a $3$ $40.125$ 3.3.568.1 None 5025.2.a.n \(2\) \(3\) \(0\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+q^{3}+(3+\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots\)
5025.2.a.r 5025.a 1.a $3$ $40.125$ 3.3.1620.1 None 5025.2.a.l \(3\) \(-3\) \(0\) \(6\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{6}+(2-\beta _{1})q^{7}+\cdots\)
5025.2.a.s 5025.a 1.a $4$ $40.125$ 4.4.9301.1 None 1005.2.a.f \(-2\) \(4\) \(0\) \(-11\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+q^{3}+(2+\beta _{2}-\beta _{3})q^{4}+\cdots\)
5025.2.a.t 5025.a 1.a $4$ $40.125$ 4.4.1957.1 None 1005.2.a.e \(0\) \(4\) \(0\) \(-1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
5025.2.a.u 5025.a 1.a $4$ $40.125$ 4.4.2525.1 None 1005.2.a.d \(2\) \(-4\) \(0\) \(1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
5025.2.a.v 5025.a 1.a $4$ $40.125$ 4.4.1957.1 None 1005.2.a.c \(4\) \(-4\) \(0\) \(9\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}-q^{3}+(1-\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
5025.2.a.w 5025.a 1.a $5$ $40.125$ 5.5.772525.1 None 1005.2.a.h \(-1\) \(-5\) \(0\) \(3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
5025.2.a.x 5025.a 1.a $5$ $40.125$ 5.5.1025428.1 None 201.2.a.e \(0\) \(-5\) \(0\) \(-7\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
5025.2.a.y 5025.a 1.a $5$ $40.125$ 5.5.273397.1 None 1005.2.a.g \(2\) \(5\) \(0\) \(9\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
5025.2.a.z 5025.a 1.a $6$ $40.125$ 6.6.5625337.1 None 5025.2.a.z \(0\) \(-6\) \(0\) \(6\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}-q^{3}+(2-\beta _{2}+\beta _{4}-\beta _{5})q^{4}+\cdots\)
5025.2.a.ba 5025.a 1.a $6$ $40.125$ 6.6.5625337.1 None 5025.2.a.z \(0\) \(6\) \(0\) \(-6\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+q^{3}+(2-\beta _{2}+\beta _{4}-\beta _{5})q^{4}+\cdots\)
5025.2.a.bb 5025.a 1.a $7$ $40.125$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 1005.2.a.i \(-4\) \(-7\) \(0\) \(-3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}-q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
5025.2.a.bc 5025.a 1.a $8$ $40.125$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 5025.2.a.bc \(-3\) \(8\) \(0\) \(-10\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+q^{3}+(\beta _{1}+\beta _{2}+\beta _{4})q^{4}+\cdots\)
5025.2.a.bd 5025.a 1.a $8$ $40.125$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 5025.2.a.bc \(3\) \(-8\) \(0\) \(10\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}-q^{3}+(\beta _{1}+\beta _{2}+\beta _{4})q^{4}+\cdots\)
5025.2.a.be 5025.a 1.a $8$ $40.125$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 1005.2.a.j \(3\) \(8\) \(0\) \(3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
5025.2.a.bf 5025.a 1.a $10$ $40.125$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 5025.2.a.bf \(-4\) \(-10\) \(0\) \(-16\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
5025.2.a.bg 5025.a 1.a $10$ $40.125$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 5025.2.a.bg \(-3\) \(-10\) \(0\) \(-12\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
5025.2.a.bh 5025.a 1.a $10$ $40.125$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 5025.2.a.bg \(3\) \(10\) \(0\) \(12\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
5025.2.a.bi 5025.a 1.a $10$ $40.125$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 5025.2.a.bf \(4\) \(10\) \(0\) \(16\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
5025.2.a.bj 5025.a 1.a $14$ $40.125$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None 1005.2.c.c \(0\) \(-14\) \(0\) \(6\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
5025.2.a.bk 5025.a 1.a $14$ $40.125$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None 1005.2.c.c \(0\) \(14\) \(0\) \(-6\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
5025.2.a.bl 5025.a 1.a $17$ $40.125$ \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None 1005.2.c.d \(-1\) \(-17\) \(0\) \(-10\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
5025.2.a.bm 5025.a 1.a $17$ $40.125$ \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None 1005.2.c.d \(1\) \(17\) \(0\) \(10\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5025))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(5025)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(67))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(201))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(335))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1005))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1675))\)\(^{\oplus 2}\)