Properties

Label 8025.2.a
Level 8025
Weight 2
Character orbit a
Rep. character \(\chi_{8025}(1,\cdot)\)
Character field \(\Q\)
Dimension 336
Newforms 44
Sturm bound 2160
Trace bound 13

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Defining parameters

Level: \( N \) = \( 8025 = 3 \cdot 5^{2} \cdot 107 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8025.a (trivial)
Character field: \(\Q\)
Newforms: \( 44 \)
Sturm bound: \(2160\)
Trace bound: \(13\)
Distinguishing \(T_p\): \(2\), \(7\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8025))\).

Total New Old
Modular forms 1092 336 756
Cusp forms 1069 336 733
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.

\(3\)\(5\)\(107\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(38\)
\(+\)\(+\)\(-\)\(-\)\(43\)
\(+\)\(-\)\(+\)\(-\)\(49\)
\(+\)\(-\)\(-\)\(+\)\(39\)
\(-\)\(+\)\(+\)\(-\)\(41\)
\(-\)\(+\)\(-\)\(+\)\(36\)
\(-\)\(-\)\(+\)\(+\)\(40\)
\(-\)\(-\)\(-\)\(-\)\(50\)
Plus space\(+\)\(153\)
Minus space\(-\)\(183\)

Trace form

\(336q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 336q^{4} \) \(\mathstrut +\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 336q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(336q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 336q^{4} \) \(\mathstrut +\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 336q^{9} \) \(\mathstrut +\mathstrut 12q^{11} \) \(\mathstrut +\mathstrut 2q^{12} \) \(\mathstrut -\mathstrut 4q^{13} \) \(\mathstrut +\mathstrut 344q^{16} \) \(\mathstrut +\mathstrut 12q^{17} \) \(\mathstrut +\mathstrut 2q^{18} \) \(\mathstrut +\mathstrut 4q^{19} \) \(\mathstrut -\mathstrut 16q^{21} \) \(\mathstrut +\mathstrut 8q^{22} \) \(\mathstrut +\mathstrut 16q^{23} \) \(\mathstrut -\mathstrut 12q^{24} \) \(\mathstrut -\mathstrut 2q^{27} \) \(\mathstrut +\mathstrut 8q^{28} \) \(\mathstrut -\mathstrut 32q^{29} \) \(\mathstrut -\mathstrut 8q^{31} \) \(\mathstrut +\mathstrut 34q^{32} \) \(\mathstrut -\mathstrut 8q^{33} \) \(\mathstrut -\mathstrut 16q^{34} \) \(\mathstrut +\mathstrut 336q^{36} \) \(\mathstrut -\mathstrut 20q^{37} \) \(\mathstrut +\mathstrut 28q^{38} \) \(\mathstrut -\mathstrut 4q^{41} \) \(\mathstrut -\mathstrut 4q^{42} \) \(\mathstrut +\mathstrut 12q^{43} \) \(\mathstrut +\mathstrut 68q^{44} \) \(\mathstrut +\mathstrut 4q^{46} \) \(\mathstrut +\mathstrut 2q^{48} \) \(\mathstrut +\mathstrut 328q^{49} \) \(\mathstrut -\mathstrut 12q^{51} \) \(\mathstrut +\mathstrut 24q^{52} \) \(\mathstrut -\mathstrut 12q^{53} \) \(\mathstrut +\mathstrut 8q^{56} \) \(\mathstrut -\mathstrut 24q^{57} \) \(\mathstrut -\mathstrut 4q^{58} \) \(\mathstrut +\mathstrut 24q^{59} \) \(\mathstrut -\mathstrut 64q^{61} \) \(\mathstrut +\mathstrut 12q^{62} \) \(\mathstrut +\mathstrut 340q^{64} \) \(\mathstrut +\mathstrut 16q^{66} \) \(\mathstrut -\mathstrut 20q^{67} \) \(\mathstrut +\mathstrut 48q^{68} \) \(\mathstrut -\mathstrut 4q^{69} \) \(\mathstrut -\mathstrut 16q^{71} \) \(\mathstrut +\mathstrut 6q^{72} \) \(\mathstrut +\mathstrut 48q^{74} \) \(\mathstrut +\mathstrut 12q^{76} \) \(\mathstrut +\mathstrut 24q^{77} \) \(\mathstrut -\mathstrut 24q^{78} \) \(\mathstrut -\mathstrut 16q^{79} \) \(\mathstrut +\mathstrut 336q^{81} \) \(\mathstrut +\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 68q^{83} \) \(\mathstrut -\mathstrut 12q^{84} \) \(\mathstrut +\mathstrut 76q^{86} \) \(\mathstrut -\mathstrut 20q^{87} \) \(\mathstrut +\mathstrut 24q^{88} \) \(\mathstrut +\mathstrut 68q^{89} \) \(\mathstrut -\mathstrut 68q^{91} \) \(\mathstrut +\mathstrut 112q^{92} \) \(\mathstrut -\mathstrut 28q^{93} \) \(\mathstrut +\mathstrut 120q^{94} \) \(\mathstrut -\mathstrut 24q^{96} \) \(\mathstrut +\mathstrut 50q^{98} \) \(\mathstrut +\mathstrut 12q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8025))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 5 107
8025.2.a.a \(1\) \(64.080\) \(\Q\) None \(-2\) \(-1\) \(0\) \(-4\) \(+\) \(+\) \(+\) \(q-2q^{2}-q^{3}+2q^{4}+2q^{6}-4q^{7}+\cdots\)
8025.2.a.b \(1\) \(64.080\) \(\Q\) None \(-2\) \(-1\) \(0\) \(1\) \(+\) \(-\) \(+\) \(q-2q^{2}-q^{3}+2q^{4}+2q^{6}+q^{7}+q^{9}+\cdots\)
8025.2.a.c \(1\) \(64.080\) \(\Q\) None \(-2\) \(1\) \(0\) \(-5\) \(-\) \(-\) \(-\) \(q-2q^{2}+q^{3}+2q^{4}-2q^{6}-5q^{7}+\cdots\)
8025.2.a.d \(1\) \(64.080\) \(\Q\) None \(-2\) \(1\) \(0\) \(-3\) \(-\) \(+\) \(-\) \(q-2q^{2}+q^{3}+2q^{4}-2q^{6}-3q^{7}+\cdots\)
8025.2.a.e \(1\) \(64.080\) \(\Q\) None \(-2\) \(1\) \(0\) \(1\) \(-\) \(-\) \(-\) \(q-2q^{2}+q^{3}+2q^{4}-2q^{6}+q^{7}+q^{9}+\cdots\)
8025.2.a.f \(1\) \(64.080\) \(\Q\) None \(-1\) \(-1\) \(0\) \(2\) \(+\) \(-\) \(+\) \(q-q^{2}-q^{3}-q^{4}+q^{6}+2q^{7}+3q^{8}+\cdots\)
8025.2.a.g \(1\) \(64.080\) \(\Q\) None \(-1\) \(1\) \(0\) \(4\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{3}-q^{4}-q^{6}+4q^{7}+3q^{8}+\cdots\)
8025.2.a.h \(1\) \(64.080\) \(\Q\) None \(0\) \(-1\) \(0\) \(1\) \(+\) \(+\) \(-\) \(q-q^{3}-2q^{4}+q^{7}+q^{9}-6q^{11}+2q^{12}+\cdots\)
8025.2.a.i \(1\) \(64.080\) \(\Q\) None \(0\) \(-1\) \(0\) \(2\) \(+\) \(+\) \(+\) \(q-q^{3}-2q^{4}+2q^{7}+q^{9}-3q^{11}+\cdots\)
8025.2.a.j \(1\) \(64.080\) \(\Q\) None \(0\) \(1\) \(0\) \(-2\) \(-\) \(-\) \(-\) \(q+q^{3}-2q^{4}-2q^{7}+q^{9}-3q^{11}+\cdots\)
8025.2.a.k \(1\) \(64.080\) \(\Q\) None \(1\) \(-1\) \(0\) \(-4\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}-q^{4}-q^{6}-4q^{7}-3q^{8}+\cdots\)
8025.2.a.l \(1\) \(64.080\) \(\Q\) None \(1\) \(1\) \(0\) \(-2\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{3}-q^{4}+q^{6}-2q^{7}-3q^{8}+\cdots\)
8025.2.a.m \(1\) \(64.080\) \(\Q\) None \(2\) \(-1\) \(0\) \(-1\) \(+\) \(-\) \(+\) \(q+2q^{2}-q^{3}+2q^{4}-2q^{6}-q^{7}+q^{9}+\cdots\)
8025.2.a.n \(1\) \(64.080\) \(\Q\) None \(2\) \(-1\) \(0\) \(5\) \(+\) \(-\) \(+\) \(q+2q^{2}-q^{3}+2q^{4}-2q^{6}+5q^{7}+\cdots\)
8025.2.a.o \(1\) \(64.080\) \(\Q\) None \(2\) \(1\) \(0\) \(-1\) \(-\) \(+\) \(-\) \(q+2q^{2}+q^{3}+2q^{4}+2q^{6}-q^{7}+q^{9}+\cdots\)
8025.2.a.p \(1\) \(64.080\) \(\Q\) None \(2\) \(1\) \(0\) \(-1\) \(-\) \(+\) \(-\) \(q+2q^{2}+q^{3}+2q^{4}+2q^{6}-q^{7}+q^{9}+\cdots\)
8025.2.a.q \(1\) \(64.080\) \(\Q\) None \(2\) \(1\) \(0\) \(4\) \(-\) \(-\) \(-\) \(q+2q^{2}+q^{3}+2q^{4}+2q^{6}+4q^{7}+\cdots\)
8025.2.a.r \(2\) \(64.080\) \(\Q(\sqrt{5}) \) None \(1\) \(-2\) \(0\) \(2\) \(+\) \(+\) \(+\) \(q+\beta q^{2}-q^{3}+(-1+\beta )q^{4}-\beta q^{6}+\cdots\)
8025.2.a.s \(2\) \(64.080\) \(\Q(\sqrt{5}) \) None \(1\) \(2\) \(0\) \(4\) \(-\) \(+\) \(-\) \(q+\beta q^{2}+q^{3}+(-1+\beta )q^{4}+\beta q^{6}+\cdots\)
8025.2.a.t \(3\) \(64.080\) \(\Q(\zeta_{18})^+\) None \(-3\) \(-3\) \(0\) \(-9\) \(+\) \(+\) \(-\) \(q+(-1+\beta _{1})q^{2}-q^{3}+(1-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
8025.2.a.u \(3\) \(64.080\) 3.3.169.1 None \(-1\) \(-3\) \(0\) \(-4\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
8025.2.a.v \(3\) \(64.080\) 3.3.169.1 None \(1\) \(3\) \(0\) \(4\) \(-\) \(-\) \(-\) \(q+(1-\beta _{1}+\beta _{2})q^{2}+q^{3}+(2-2\beta _{1}+\cdots)q^{4}+\cdots\)
8025.2.a.w \(4\) \(64.080\) 4.4.1957.1 None \(3\) \(-4\) \(0\) \(8\) \(+\) \(+\) \(-\) \(q+(1+\beta _{2})q^{2}-q^{3}+(1-\beta _{1}-\beta _{3})q^{4}+\cdots\)
8025.2.a.x \(5\) \(64.080\) 5.5.240133.1 None \(-2\) \(5\) \(0\) \(-4\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
8025.2.a.y \(5\) \(64.080\) 5.5.81509.1 None \(1\) \(-5\) \(0\) \(3\) \(+\) \(+\) \(+\) \(q+\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}-\beta _{1}q^{6}+(\beta _{2}+\cdots)q^{7}+\cdots\)
8025.2.a.z \(5\) \(64.080\) 5.5.805501.1 None \(1\) \(5\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
8025.2.a.ba \(6\) \(64.080\) 6.6.13231312.1 None \(-3\) \(-6\) \(0\) \(0\) \(+\) \(+\) \(-\) \(q-\beta _{2}q^{2}-q^{3}+(1-\beta _{4})q^{4}+\beta _{2}q^{6}+\cdots\)
8025.2.a.bb \(7\) \(64.080\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(7\) \(0\) \(-6\) \(-\) \(+\) \(+\) \(q-\beta _{5}q^{2}+q^{3}+(2-\beta _{1}-\beta _{4})q^{4}-\beta _{5}q^{6}+\cdots\)
8025.2.a.bc \(10\) \(64.080\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-2\) \(10\) \(0\) \(0\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
8025.2.a.bd \(11\) \(64.080\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(4\) \(-11\) \(0\) \(4\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
8025.2.a.be \(11\) \(64.080\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(4\) \(11\) \(0\) \(9\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
8025.2.a.bf \(12\) \(64.080\) \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-3\) \(-12\) \(0\) \(-7\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
8025.2.a.bg \(13\) \(64.080\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(-1\) \(-13\) \(0\) \(-2\) \(+\) \(+\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
8025.2.a.bh \(13\) \(64.080\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(1\) \(13\) \(0\) \(2\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
8025.2.a.bi \(16\) \(64.080\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-6\) \(16\) \(0\) \(-10\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{3}+\beta _{4})q^{4}+\cdots\)
8025.2.a.bj \(16\) \(64.080\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(6\) \(-16\) \(0\) \(10\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{3}+\beta _{4})q^{4}+\cdots\)
8025.2.a.bk \(17\) \(64.080\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(-4\) \(-17\) \(0\) \(-9\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
8025.2.a.bl \(17\) \(64.080\) \(\mathbb{Q}[x]/(x^{17} - \cdots)\) None \(4\) \(17\) \(0\) \(9\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
8025.2.a.bm \(18\) \(64.080\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-4\) \(18\) \(0\) \(-12\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
8025.2.a.bn \(18\) \(64.080\) \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(4\) \(-18\) \(0\) \(12\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
8025.2.a.bo \(22\) \(64.080\) None \(-3\) \(22\) \(0\) \(-2\) \(-\) \(-\) \(+\)
8025.2.a.bp \(22\) \(64.080\) None \(3\) \(-22\) \(0\) \(2\) \(+\) \(-\) \(-\)
8025.2.a.bq \(29\) \(64.080\) None \(-6\) \(-29\) \(0\) \(-4\) \(+\) \(-\) \(+\)
8025.2.a.br \(29\) \(64.080\) None \(6\) \(29\) \(0\) \(4\) \(-\) \(-\) \(-\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8025))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(8025)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(107))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(321))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(535))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1605))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2675))\)\(^{\oplus 2}\)