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Properties

Label 3025.2.a
Level $3025$
Weight $2$
Character orbit 3025.a
Rep. character $\chi_{3025}(1,\cdot)$
Character field $\Q$
Dimension $159$
Newform subspaces $41$
Sturm bound $660$
Trace bound $6$

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Defining parameters

Level: \( N \) \(=\) \( 3025 = 5^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3025.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 41 \)
Sturm bound: \(660\)
Trace bound: \(6\)
Distinguishing \(T_p\): \(2\), \(3\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3025))\).

Total New Old
Modular forms 366 186 180
Cusp forms 295 159 136
Eisenstein series 71 27 44

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(5\)\(11\)FrickeDim
\(+\)\(+\)$+$\(37\)
\(+\)\(-\)$-$\(40\)
\(-\)\(+\)$-$\(44\)
\(-\)\(-\)$+$\(38\)
Plus space\(+\)\(75\)
Minus space\(-\)\(84\)

Trace form

\( 159 q + q^{2} - 2 q^{3} + 147 q^{4} + 2 q^{6} - 6 q^{7} + 3 q^{8} + 133 q^{9} + O(q^{10}) \) \( 159 q + q^{2} - 2 q^{3} + 147 q^{4} + 2 q^{6} - 6 q^{7} + 3 q^{8} + 133 q^{9} - 12 q^{12} - 2 q^{13} + 4 q^{14} + 123 q^{16} + 12 q^{17} + 11 q^{18} - 8 q^{19} + 6 q^{21} + 14 q^{23} + 16 q^{24} - 4 q^{26} - 2 q^{27} - 8 q^{28} + 6 q^{29} - 2 q^{31} + 7 q^{32} + 40 q^{34} + 123 q^{36} - 2 q^{37} + 8 q^{38} - 24 q^{39} + 2 q^{41} + 56 q^{42} - 14 q^{43} + 30 q^{46} - 4 q^{47} + 24 q^{48} + 59 q^{49} + 2 q^{51} + 14 q^{52} - 4 q^{53} + 6 q^{54} - 20 q^{56} - 12 q^{58} + 18 q^{59} + 6 q^{61} - 22 q^{62} - 16 q^{63} + 63 q^{64} - 14 q^{67} + 14 q^{68} + 46 q^{69} + 18 q^{71} + 39 q^{72} + 10 q^{73} - 24 q^{74} + 8 q^{76} + 40 q^{78} - 22 q^{79} + 95 q^{81} + 16 q^{82} - 22 q^{83} + 64 q^{84} + 68 q^{86} + 32 q^{87} + 54 q^{89} - 88 q^{91} - 46 q^{93} - 64 q^{94} - 4 q^{96} - 30 q^{97} - 7 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3025))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5 11
3025.2.a.a 3025.a 1.a $1$ $24.155$ \(\Q\) None \(-2\) \(1\) \(0\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}-2q^{6}-2q^{7}+\cdots\)
3025.2.a.b 3025.a 1.a $1$ $24.155$ \(\Q\) None \(-1\) \(-2\) \(0\) \(2\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}-q^{4}+2q^{6}+2q^{7}+3q^{8}+\cdots\)
3025.2.a.c 3025.a 1.a $1$ $24.155$ \(\Q\) None \(-1\) \(3\) \(0\) \(-3\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+3q^{3}-q^{4}-3q^{6}-3q^{7}+3q^{8}+\cdots\)
3025.2.a.d 3025.a 1.a $1$ $24.155$ \(\Q\) \(\Q(\sqrt{-11}) \) \(0\) \(1\) \(0\) \(0\) $+$ $+$ $N(\mathrm{U}(1))$ \(q+q^{3}-2q^{4}-2q^{9}-2q^{12}+4q^{16}+\cdots\)
3025.2.a.e 3025.a 1.a $1$ $24.155$ \(\Q\) None \(1\) \(-2\) \(0\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}-q^{4}-2q^{6}-2q^{7}-3q^{8}+\cdots\)
3025.2.a.f 3025.a 1.a $1$ $24.155$ \(\Q\) None \(1\) \(0\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-3q^{8}-3q^{9}+2q^{13}+\cdots\)
3025.2.a.g 3025.a 1.a $1$ $24.155$ \(\Q\) None \(1\) \(3\) \(0\) \(3\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+3q^{3}-q^{4}+3q^{6}+3q^{7}-3q^{8}+\cdots\)
3025.2.a.h 3025.a 1.a $2$ $24.155$ \(\Q(\sqrt{13}) \) None \(-1\) \(1\) \(0\) \(-5\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(1-\beta )q^{3}+(1+\beta )q^{4}+3q^{6}+\cdots\)
3025.2.a.i 3025.a 1.a $2$ $24.155$ \(\Q(\sqrt{5}) \) None \(-1\) \(3\) \(0\) \(-1\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(1+\beta )q^{3}+(-1+\beta )q^{4}+(-1+\cdots)q^{6}+\cdots\)
3025.2.a.j 3025.a 1.a $2$ $24.155$ \(\Q(\sqrt{3}) \) None \(0\) \(-4\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-2q^{3}+q^{4}-2\beta q^{6}+2\beta q^{7}+\cdots\)
3025.2.a.k 3025.a 1.a $2$ $24.155$ \(\Q(\sqrt{11}) \) \(\Q(\sqrt{-11}) \) \(0\) \(0\) \(0\) \(0\) $-$ $+$ $N(\mathrm{U}(1))$ \(q-\beta q^{3}-2q^{4}+8q^{9}+2\beta q^{12}+4q^{16}+\cdots\)
3025.2.a.l 3025.a 1.a $2$ $24.155$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+q^{4}+\beta q^{6}-\beta q^{7}-\beta q^{8}+\cdots\)
3025.2.a.m 3025.a 1.a $2$ $24.155$ \(\Q(\sqrt{5}) \) None \(1\) \(-3\) \(0\) \(1\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1-\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
3025.2.a.n 3025.a 1.a $2$ $24.155$ \(\Q(\sqrt{13}) \) None \(1\) \(-1\) \(0\) \(5\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1+\beta )q^{3}+(1+\beta )q^{4}+3q^{6}+\cdots\)
3025.2.a.o 3025.a 1.a $2$ $24.155$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(-4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+2\beta q^{3}+(1+2\beta )q^{4}+(4+\cdots)q^{6}+\cdots\)
3025.2.a.p 3025.a 1.a $3$ $24.155$ 3.3.404.1 None \(-1\) \(-1\) \(0\) \(1\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}-\beta _{1}q^{3}+(3+\beta _{1}-\beta _{2})q^{4}+\cdots\)
3025.2.a.q 3025.a 1.a $3$ $24.155$ 3.3.473.1 None \(0\) \(-3\) \(0\) \(4\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-1-\beta _{1})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
3025.2.a.r 3025.a 1.a $3$ $24.155$ 3.3.473.1 None \(0\) \(-3\) \(0\) \(-4\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1-\beta _{1})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
3025.2.a.s 3025.a 1.a $3$ $24.155$ 3.3.473.1 None \(0\) \(3\) \(0\) \(-4\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{1})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
3025.2.a.t 3025.a 1.a $3$ $24.155$ 3.3.473.1 None \(0\) \(3\) \(0\) \(4\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{1})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
3025.2.a.u 3025.a 1.a $3$ $24.155$ 3.3.404.1 None \(1\) \(-1\) \(0\) \(-1\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}-\beta _{1}q^{3}+(3+\beta _{1}-\beta _{2})q^{4}+\cdots\)
3025.2.a.v 3025.a 1.a $4$ $24.155$ 4.4.2525.1 None \(-3\) \(2\) \(0\) \(-11\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{3})q^{2}+\beta _{1}q^{3}+(1+\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
3025.2.a.w 3025.a 1.a $4$ $24.155$ 4.4.725.1 None \(-1\) \(0\) \(0\) \(-3\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1-\beta _{2}-\beta _{3})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots\)
3025.2.a.x 3025.a 1.a $4$ $24.155$ 4.4.105840.1 None \(0\) \(-2\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+(3+\beta _{2})q^{4}+\cdots\)
3025.2.a.y 3025.a 1.a $4$ $24.155$ \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+\beta _{2}q^{4}-q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
3025.2.a.z 3025.a 1.a $4$ $24.155$ \(\Q(\zeta_{24})^+\) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+\beta _{2}q^{4}+q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
3025.2.a.ba 3025.a 1.a $4$ $24.155$ \(\Q(\sqrt{3}, \sqrt{11})\) None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(2+\beta _{3})q^{4}+\cdots\)
3025.2.a.bb 3025.a 1.a $4$ $24.155$ 4.4.4400.1 \(\Q(\sqrt{-55}) \) \(0\) \(0\) \(0\) \(0\) $-$ $+$ $N(\mathrm{U}(1))$ \(q-\beta _{2}q^{2}+(2-\beta _{3})q^{4}+\beta _{1}q^{7}+(\beta _{1}+\cdots)q^{8}+\cdots\)
3025.2.a.bc 3025.a 1.a $4$ $24.155$ 4.4.105840.1 None \(0\) \(2\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{3}+(3+\beta _{2})q^{4}+\cdots\)
3025.2.a.bd 3025.a 1.a $4$ $24.155$ 4.4.725.1 None \(1\) \(0\) \(0\) \(3\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1-\beta _{2}-\beta _{3})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots\)
3025.2.a.be 3025.a 1.a $4$ $24.155$ 4.4.2525.1 None \(3\) \(2\) \(0\) \(11\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2}-\beta _{3})q^{2}+(1-\beta _{1})q^{3}+(2+\cdots)q^{4}+\cdots\)
3025.2.a.bf 3025.a 1.a $6$ $24.155$ \(\Q(\zeta_{36})^+\) None \(0\) \(-6\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-1-\beta _{4})q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
3025.2.a.bg 3025.a 1.a $6$ $24.155$ 6.6.27433728.1 None \(0\) \(-6\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-1+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
3025.2.a.bh 3025.a 1.a $6$ $24.155$ \(\Q(\zeta_{36})^+\) None \(0\) \(6\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{4})q^{3}+\beta _{2}q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots\)
3025.2.a.bi 3025.a 1.a $8$ $24.155$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-5\) \(-1\) \(0\) \(-8\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+\beta _{5}q^{3}+(1-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
3025.2.a.bj 3025.a 1.a $8$ $24.155$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-5\) \(1\) \(0\) \(-8\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}-\beta _{5}q^{3}+(1-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
3025.2.a.bk 3025.a 1.a $8$ $24.155$ 8.8.1480160000.1 None \(0\) \(0\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{6}-\beta _{7})q^{3}+\beta _{2}q^{4}+\cdots\)
3025.2.a.bl 3025.a 1.a $8$ $24.155$ 8.8.1480160000.1 None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{6}+\beta _{7})q^{3}+\beta _{2}q^{4}+\cdots\)
3025.2.a.bm 3025.a 1.a $8$ $24.155$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(5\) \(-1\) \(0\) \(8\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+\beta _{5}q^{3}+(1-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
3025.2.a.bn 3025.a 1.a $8$ $24.155$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(5\) \(1\) \(0\) \(8\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}-\beta _{5}q^{3}+(1-\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
3025.2.a.bo 3025.a 1.a $12$ $24.155$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(2-\beta _{10})q^{4}+\beta _{2}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3025))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3025)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(275))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(605))\)\(^{\oplus 2}\)