Properties

Label 3525.2.a
Level $3525$
Weight $2$
Character orbit 3525.a
Rep. character $\chi_{3525}(1,\cdot)$
Character field $\Q$
Dimension $146$
Newform subspaces $35$
Sturm bound $960$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3525.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 35 \)
Sturm bound: \(960\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3525))\).

Total New Old
Modular forms 492 146 346
Cusp forms 469 146 323
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.

\(3\)\(5\)\(47\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(17\)
\(+\)\(+\)\(-\)\(-\)\(19\)
\(+\)\(-\)\(+\)\(-\)\(21\)
\(+\)\(-\)\(-\)\(+\)\(17\)
\(-\)\(+\)\(+\)\(-\)\(17\)
\(-\)\(+\)\(-\)\(+\)\(15\)
\(-\)\(-\)\(+\)\(+\)\(18\)
\(-\)\(-\)\(-\)\(-\)\(22\)
Plus space\(+\)\(67\)
Minus space\(-\)\(79\)

Trace form

\( 146q - 2q^{2} - 2q^{3} + 142q^{4} + 2q^{6} - 4q^{7} - 6q^{8} + 146q^{9} + O(q^{10}) \) \( 146q - 2q^{2} - 2q^{3} + 142q^{4} + 2q^{6} - 4q^{7} - 6q^{8} + 146q^{9} - 8q^{11} - 6q^{12} + 4q^{13} + 12q^{14} + 150q^{16} + 16q^{17} - 2q^{18} - 8q^{19} - 12q^{21} + 24q^{22} - 8q^{23} + 6q^{24} - 12q^{26} - 2q^{27} - 16q^{28} - 32q^{29} - 14q^{32} + 16q^{33} + 12q^{34} + 142q^{36} - 16q^{37} - 12q^{38} - 16q^{39} - 16q^{41} + 20q^{42} - 4q^{43} - 56q^{44} - 80q^{46} - 14q^{48} + 154q^{49} + 8q^{51} + 20q^{52} + 2q^{54} - 32q^{56} - 12q^{57} + 8q^{58} + 60q^{59} - 16q^{61} + 12q^{62} - 4q^{63} + 78q^{64} - 16q^{66} + 4q^{67} + 36q^{68} + 8q^{69} + 40q^{71} - 6q^{72} + 12q^{73} - 48q^{74} - 44q^{76} - 28q^{78} - 20q^{79} + 146q^{81} + 44q^{83} - 24q^{84} - 12q^{86} + 16q^{87} + 32q^{88} + 4q^{89} - 36q^{91} - 16q^{92} + 12q^{93} + 8q^{94} + 14q^{96} + 32q^{97} + 26q^{98} - 8q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3525))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 3 5 47
3525.2.a.a \(1\) \(28.147\) \(\Q\) None \(-2\) \(-1\) \(0\) \(-4\) \(+\) \(-\) \(+\) \(q-2q^{2}-q^{3}+2q^{4}+2q^{6}-4q^{7}+\cdots\)
3525.2.a.b \(1\) \(28.147\) \(\Q\) None \(-2\) \(-1\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(q-2q^{2}-q^{3}+2q^{4}+2q^{6}-q^{7}+q^{9}+\cdots\)
3525.2.a.c \(1\) \(28.147\) \(\Q\) None \(-2\) \(-1\) \(0\) \(3\) \(+\) \(+\) \(-\) \(q-2q^{2}-q^{3}+2q^{4}+2q^{6}+3q^{7}+\cdots\)
3525.2.a.d \(1\) \(28.147\) \(\Q\) None \(-1\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}-q^{4}+q^{6}+3q^{8}+q^{9}+\cdots\)
3525.2.a.e \(1\) \(28.147\) \(\Q\) None \(-1\) \(-1\) \(0\) \(3\) \(+\) \(+\) \(+\) \(q-q^{2}-q^{3}-q^{4}+q^{6}+3q^{7}+3q^{8}+\cdots\)
3525.2.a.f \(1\) \(28.147\) \(\Q\) None \(0\) \(-1\) \(0\) \(-2\) \(+\) \(+\) \(-\) \(q-q^{3}-2q^{4}-2q^{7}+q^{9}-6q^{11}+\cdots\)
3525.2.a.g \(1\) \(28.147\) \(\Q\) None \(0\) \(1\) \(0\) \(-2\) \(-\) \(+\) \(-\) \(q+q^{3}-2q^{4}-2q^{7}+q^{9}+2q^{11}+\cdots\)
3525.2.a.h \(1\) \(28.147\) \(\Q\) None \(0\) \(1\) \(0\) \(3\) \(-\) \(+\) \(-\) \(q+q^{3}-2q^{4}+3q^{7}+q^{9}-3q^{11}+\cdots\)
3525.2.a.i \(1\) \(28.147\) \(\Q\) None \(1\) \(-1\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(q+q^{2}-q^{3}-q^{4}-q^{6}-q^{7}-3q^{8}+\cdots\)
3525.2.a.j \(1\) \(28.147\) \(\Q\) None \(1\) \(-1\) \(0\) \(0\) \(+\) \(+\) \(-\) \(q+q^{2}-q^{3}-q^{4}-q^{6}-3q^{8}+q^{9}+\cdots\)
3525.2.a.k \(1\) \(28.147\) \(\Q\) None \(1\) \(1\) \(0\) \(-4\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}-q^{4}+q^{6}-4q^{7}-3q^{8}+\cdots\)
3525.2.a.l \(1\) \(28.147\) \(\Q\) None \(1\) \(1\) \(0\) \(5\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{3}-q^{4}+q^{6}+5q^{7}-3q^{8}+\cdots\)
3525.2.a.m \(1\) \(28.147\) \(\Q\) None \(2\) \(-1\) \(0\) \(3\) \(+\) \(+\) \(+\) \(q+2q^{2}-q^{3}+2q^{4}-2q^{6}+3q^{7}+\cdots\)
3525.2.a.n \(1\) \(28.147\) \(\Q\) None \(2\) \(1\) \(0\) \(1\) \(-\) \(-\) \(-\) \(q+2q^{2}+q^{3}+2q^{4}+2q^{6}+q^{7}+q^{9}+\cdots\)
3525.2.a.o \(1\) \(28.147\) \(\Q\) None \(2\) \(1\) \(0\) \(4\) \(-\) \(-\) \(-\) \(q+2q^{2}+q^{3}+2q^{4}+2q^{6}+4q^{7}+\cdots\)
3525.2.a.p \(2\) \(28.147\) \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(0\) \(2\) \(-\) \(+\) \(-\) \(q+\beta q^{2}+q^{3}+q^{4}+\beta q^{6}+q^{7}-\beta q^{8}+\cdots\)
3525.2.a.q \(2\) \(28.147\) \(\Q(\sqrt{17}) \) None \(1\) \(2\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(q+\beta q^{2}+q^{3}+(2+\beta )q^{4}+\beta q^{6}+(-1+\cdots)q^{7}+\cdots\)
3525.2.a.r \(2\) \(28.147\) \(\Q(\sqrt{17}) \) None \(1\) \(2\) \(0\) \(3\) \(-\) \(+\) \(+\) \(q+\beta q^{2}+q^{3}+(2+\beta )q^{4}+\beta q^{6}+(2+\cdots)q^{7}+\cdots\)
3525.2.a.s \(2\) \(28.147\) \(\Q(\sqrt{2}) \) None \(2\) \(-2\) \(0\) \(6\) \(+\) \(+\) \(-\) \(q+(1+\beta )q^{2}-q^{3}+(1+2\beta )q^{4}+(-1+\cdots)q^{6}+\cdots\)
3525.2.a.t \(4\) \(28.147\) 4.4.4352.1 None \(-4\) \(4\) \(0\) \(-8\) \(-\) \(+\) \(-\) \(q+(-1-\beta _{1}+\beta _{3})q^{2}+q^{3}+(2+\beta _{1}+\cdots)q^{4}+\cdots\)
3525.2.a.u \(4\) \(28.147\) 4.4.14656.1 None \(-2\) \(4\) \(0\) \(0\) \(-\) \(+\) \(+\) \(q+(-1+\beta _{1})q^{2}+q^{3}+(2-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
3525.2.a.v \(5\) \(28.147\) 5.5.2379008.1 None \(0\) \(-5\) \(0\) \(-10\) \(+\) \(+\) \(+\) \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
3525.2.a.w \(6\) \(28.147\) 6.6.414764096.1 None \(-2\) \(-6\) \(0\) \(-4\) \(+\) \(+\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
3525.2.a.x \(7\) \(28.147\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-3\) \(-7\) \(0\) \(-5\) \(+\) \(-\) \(-\) \(q-\beta _{1}q^{2}-q^{3}+(\beta _{1}+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
3525.2.a.y \(7\) \(28.147\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-1\) \(7\) \(0\) \(-11\) \(-\) \(+\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
3525.2.a.z \(7\) \(28.147\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(-1\) \(7\) \(0\) \(7\) \(-\) \(-\) \(-\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2}+\beta _{3})q^{4}-\beta _{1}q^{6}+\cdots\)
3525.2.a.ba \(7\) \(28.147\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(1\) \(-7\) \(0\) \(-7\) \(+\) \(+\) \(+\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2}+\beta _{3})q^{4}-\beta _{1}q^{6}+\cdots\)
3525.2.a.bb \(7\) \(28.147\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(1\) \(-7\) \(0\) \(11\) \(+\) \(-\) \(+\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{1}+\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
3525.2.a.bc \(7\) \(28.147\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(3\) \(7\) \(0\) \(5\) \(-\) \(+\) \(+\) \(q+\beta _{1}q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
3525.2.a.bd \(8\) \(28.147\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-3\) \(8\) \(0\) \(-8\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
3525.2.a.be \(8\) \(28.147\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(3\) \(-8\) \(0\) \(8\) \(+\) \(+\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
3525.2.a.bf \(10\) \(28.147\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(-3\) \(10\) \(0\) \(0\) \(-\) \(-\) \(+\) \(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
3525.2.a.bg \(10\) \(28.147\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(3\) \(-10\) \(0\) \(0\) \(+\) \(-\) \(-\) \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
3525.2.a.bh \(13\) \(28.147\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(-3\) \(-13\) \(0\) \(4\) \(+\) \(-\) \(+\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)
3525.2.a.bi \(13\) \(28.147\) \(\mathbb{Q}[x]/(x^{13} - \cdots)\) None \(3\) \(13\) \(0\) \(-4\) \(-\) \(-\) \(-\) \(q+\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}+\beta _{1}q^{6}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3525))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3525)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(47))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(141))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(235))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(705))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1175))\)\(^{\oplus 2}\)