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Properties

Label 2535.2.a
Level $2535$
Weight $2$
Character orbit 2535.a
Rep. character $\chi_{2535}(1,\cdot)$
Character field $\Q$
Dimension $104$
Newform subspaces $40$
Sturm bound $728$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 2535 = 3 \cdot 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2535.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 40 \)
Sturm bound: \(728\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(2\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2535))\).

Total New Old
Modular forms 392 104 288
Cusp forms 337 104 233
Eisenstein series 55 0 55

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

\(3\)\(5\)\(13\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(11\)
\(+\)\(+\)\(-\)\(-\)\(14\)
\(+\)\(-\)\(+\)\(-\)\(18\)
\(+\)\(-\)\(-\)\(+\)\(8\)
\(-\)\(+\)\(+\)\(-\)\(15\)
\(-\)\(+\)\(-\)\(+\)\(12\)
\(-\)\(-\)\(+\)\(+\)\(8\)
\(-\)\(-\)\(-\)\(-\)\(18\)
Plus space\(+\)\(39\)
Minus space\(-\)\(65\)

Trace form

\( 104 q - 4 q^{2} + 2 q^{3} + 100 q^{4} - 2 q^{6} - 12 q^{8} + 104 q^{9} + O(q^{10}) \) \( 104 q - 4 q^{2} + 2 q^{3} + 100 q^{4} - 2 q^{6} - 12 q^{8} + 104 q^{9} + 6 q^{12} + 16 q^{14} - 2 q^{15} + 100 q^{16} + 8 q^{17} - 4 q^{18} + 8 q^{20} + 8 q^{21} + 16 q^{22} + 6 q^{24} + 104 q^{25} + 2 q^{27} + 32 q^{28} - 16 q^{29} + 2 q^{30} + 8 q^{31} + 12 q^{32} - 8 q^{33} + 32 q^{34} + 100 q^{36} - 24 q^{37} + 48 q^{38} + 8 q^{42} + 8 q^{43} + 32 q^{44} + 32 q^{46} + 8 q^{47} + 30 q^{48} + 128 q^{49} - 4 q^{50} + 4 q^{51} - 8 q^{53} - 2 q^{54} + 16 q^{55} + 40 q^{56} + 16 q^{57} - 24 q^{58} + 16 q^{59} - 6 q^{60} + 16 q^{61} + 8 q^{62} + 116 q^{64} - 16 q^{67} + 40 q^{68} - 16 q^{69} - 8 q^{70} - 12 q^{72} - 8 q^{73} + 24 q^{74} + 2 q^{75} + 8 q^{76} - 8 q^{77} + 8 q^{79} + 32 q^{80} + 104 q^{81} + 24 q^{82} - 8 q^{83} - 16 q^{84} - 16 q^{85} - 40 q^{86} + 12 q^{87} + 40 q^{88} + 32 q^{92} + 8 q^{93} + 24 q^{94} + 30 q^{96} + 8 q^{97} - 20 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2535))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 5 13
2535.2.a.a 2535.a 1.a $1$ $20.242$ \(\Q\) None \(-2\) \(-1\) \(-1\) \(-3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-q^{3}+2q^{4}-q^{5}+2q^{6}-3q^{7}+\cdots\)
2535.2.a.b 2535.a 1.a $1$ $20.242$ \(\Q\) None \(-2\) \(1\) \(-1\) \(3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}-q^{5}-2q^{6}+3q^{7}+\cdots\)
2535.2.a.c 2535.a 1.a $1$ $20.242$ \(\Q\) None \(-2\) \(1\) \(1\) \(-5\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}-5q^{7}+\cdots\)
2535.2.a.d 2535.a 1.a $1$ $20.242$ \(\Q\) None \(-2\) \(1\) \(1\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+q^{3}+2q^{4}+q^{5}-2q^{6}+q^{7}+\cdots\)
2535.2.a.e 2535.a 1.a $1$ $20.242$ \(\Q\) None \(-1\) \(1\) \(-1\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-q^{5}-q^{6}-2q^{7}+\cdots\)
2535.2.a.f 2535.a 1.a $1$ $20.242$ \(\Q\) None \(0\) \(-1\) \(-1\) \(3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}-q^{5}+3q^{7}+q^{9}-3q^{11}+\cdots\)
2535.2.a.g 2535.a 1.a $1$ $20.242$ \(\Q\) None \(0\) \(-1\) \(1\) \(-3\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{4}+q^{5}-3q^{7}+q^{9}+3q^{11}+\cdots\)
2535.2.a.h 2535.a 1.a $1$ $20.242$ \(\Q\) None \(0\) \(1\) \(-1\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}-q^{5}-q^{7}+q^{9}+6q^{11}+\cdots\)
2535.2.a.i 2535.a 1.a $1$ $20.242$ \(\Q\) None \(0\) \(1\) \(1\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{4}+q^{5}+q^{7}+q^{9}-6q^{11}+\cdots\)
2535.2.a.j 2535.a 1.a $1$ $20.242$ \(\Q\) None \(1\) \(-1\) \(-1\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}-q^{4}-q^{5}-q^{6}-3q^{8}+\cdots\)
2535.2.a.k 2535.a 1.a $1$ $20.242$ \(\Q\) None \(1\) \(1\) \(-1\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}-q^{5}+q^{6}-3q^{8}+\cdots\)
2535.2.a.l 2535.a 1.a $1$ $20.242$ \(\Q\) None \(1\) \(1\) \(1\) \(2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}+q^{5}+q^{6}+2q^{7}+\cdots\)
2535.2.a.m 2535.a 1.a $1$ $20.242$ \(\Q\) None \(2\) \(1\) \(-1\) \(5\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+2q^{4}-q^{5}+2q^{6}+5q^{7}+\cdots\)
2535.2.a.n 2535.a 1.a $2$ $20.242$ \(\Q(\sqrt{3}) \) None \(-2\) \(2\) \(-2\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+q^{3}+(2-2\beta )q^{4}-q^{5}+\cdots\)
2535.2.a.o 2535.a 1.a $2$ $20.242$ \(\Q(\sqrt{3}) \) None \(-2\) \(2\) \(2\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+q^{3}+(2-2\beta )q^{4}+q^{5}+\cdots\)
2535.2.a.p 2535.a 1.a $2$ $20.242$ \(\Q(\sqrt{17}) \) None \(-1\) \(2\) \(-2\) \(3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+q^{3}+(2+\beta )q^{4}-q^{5}-\beta q^{6}+\cdots\)
2535.2.a.q 2535.a 1.a $2$ $20.242$ \(\Q(\sqrt{17}) \) None \(1\) \(2\) \(2\) \(-3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{3}+(2+\beta )q^{4}+q^{5}+\beta q^{6}+\cdots\)
2535.2.a.r 2535.a 1.a $2$ $20.242$ \(\Q(\sqrt{3}) \) None \(2\) \(2\) \(-2\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+q^{3}+(2+2\beta )q^{4}-q^{5}+\cdots\)
2535.2.a.s 2535.a 1.a $2$ $20.242$ \(\Q(\sqrt{3}) \) None \(2\) \(2\) \(2\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+q^{3}+(2+2\beta )q^{4}+q^{5}+\cdots\)
2535.2.a.t 2535.a 1.a $3$ $20.242$ \(\Q(\zeta_{14})^+\) None \(-3\) \(3\) \(3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1}+\beta _{2})q^{2}+q^{3}+(4-\beta _{1}+\cdots)q^{4}+\cdots\)
2535.2.a.u 2535.a 1.a $3$ $20.242$ \(\Q(\zeta_{14})^+\) None \(-2\) \(3\) \(-3\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+q^{3}+(\beta _{1}+\beta _{2})q^{4}+\cdots\)
2535.2.a.v 2535.a 1.a $3$ $20.242$ \(\Q(\zeta_{14})^+\) None \(-1\) \(-3\) \(3\) \(2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
2535.2.a.w 2535.a 1.a $3$ $20.242$ \(\Q(\zeta_{14})^+\) None \(-1\) \(3\) \(-3\) \(4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
2535.2.a.x 2535.a 1.a $3$ $20.242$ \(\Q(\zeta_{14})^+\) None \(-1\) \(3\) \(3\) \(12\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
2535.2.a.y 2535.a 1.a $3$ $20.242$ 3.3.148.1 None \(0\) \(-3\) \(-3\) \(-5\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}-q^{3}+(1-\beta _{1}-\beta _{2})q^{4}-q^{5}+\cdots\)
2535.2.a.z 2535.a 1.a $3$ $20.242$ 3.3.148.1 None \(0\) \(-3\) \(3\) \(5\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}-q^{3}+(1-\beta _{1}-\beta _{2})q^{4}+q^{5}+\cdots\)
2535.2.a.ba 2535.a 1.a $3$ $20.242$ 3.3.756.1 None \(0\) \(-3\) \(-3\) \(-3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
2535.2.a.bb 2535.a 1.a $3$ $20.242$ 3.3.756.1 None \(0\) \(-3\) \(3\) \(3\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(2+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
2535.2.a.bc 2535.a 1.a $3$ $20.242$ 3.3.316.1 None \(0\) \(-3\) \(3\) \(-1\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(3+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
2535.2.a.bd 2535.a 1.a $3$ $20.242$ \(\Q(\zeta_{14})^+\) None \(1\) \(-3\) \(-3\) \(-2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
2535.2.a.be 2535.a 1.a $3$ $20.242$ \(\Q(\zeta_{14})^+\) None \(1\) \(3\) \(-3\) \(-12\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
2535.2.a.bf 2535.a 1.a $3$ $20.242$ \(\Q(\zeta_{14})^+\) None \(1\) \(3\) \(3\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
2535.2.a.bg 2535.a 1.a $3$ $20.242$ \(\Q(\zeta_{14})^+\) None \(2\) \(3\) \(3\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+q^{3}+(1-2\beta _{1}+\beta _{2})q^{4}+\cdots\)
2535.2.a.bh 2535.a 1.a $3$ $20.242$ \(\Q(\zeta_{14})^+\) None \(3\) \(3\) \(-3\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1}-\beta _{2})q^{2}+q^{3}+(4-\beta _{1})q^{4}+\cdots\)
2535.2.a.bi 2535.a 1.a $4$ $20.242$ 4.4.7488.1 None \(-2\) \(4\) \(-4\) \(-6\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{2}+q^{3}+(1-\beta _{2})q^{4}-q^{5}+\beta _{3}q^{6}+\cdots\)
2535.2.a.bj 2535.a 1.a $4$ $20.242$ 4.4.13824.1 None \(0\) \(-4\) \(-4\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
2535.2.a.bk 2535.a 1.a $4$ $20.242$ 4.4.13824.1 None \(0\) \(-4\) \(4\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
2535.2.a.bl 2535.a 1.a $4$ $20.242$ 4.4.7488.1 None \(2\) \(4\) \(4\) \(6\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{2}+q^{3}+(1-\beta _{2})q^{4}+q^{5}-\beta _{3}q^{6}+\cdots\)
2535.2.a.bm 2535.a 1.a $9$ $20.242$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(-9\) \(-9\) \(10\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{7}q^{2}-q^{3}+(1+\beta _{1}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
2535.2.a.bn 2535.a 1.a $9$ $20.242$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None \(0\) \(-9\) \(9\) \(-10\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{7}q^{2}-q^{3}+(1+\beta _{1}-\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2535))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2535)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(195))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(507))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(845))\)\(^{\oplus 2}\)