Properties

Label 7803.2.a
Level $7803$
Weight $2$
Character orbit 7803.a
Rep. character $\chi_{7803}(1,\cdot)$
Character field $\Q$
Dimension $361$
Newform subspaces $59$
Sturm bound $1836$
Trace bound $73$

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Defining parameters

Level: \( N \) \(=\) \( 7803 = 3^{3} \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7803.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 59 \)
Sturm bound: \(1836\)
Trace bound: \(73\)
Distinguishing \(T_p\): \(2\), \(5\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7803))\).

Total New Old
Modular forms 972 361 611
Cusp forms 865 361 504
Eisenstein series 107 0 107

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

\(3\)\(17\)FrickeDim.
\(+\)\(+\)\(+\)\(84\)
\(+\)\(-\)\(-\)\(96\)
\(-\)\(+\)\(-\)\(96\)
\(-\)\(-\)\(+\)\(85\)
Plus space\(+\)\(169\)
Minus space\(-\)\(192\)

Trace form

\( 361 q + 362 q^{4} - q^{7} + O(q^{10}) \) \( 361 q + 362 q^{4} - q^{7} - 12 q^{10} - 7 q^{13} + 376 q^{16} + 5 q^{19} + 20 q^{22} + 351 q^{25} + 30 q^{28} + 16 q^{31} - 17 q^{37} - 56 q^{40} - 8 q^{43} + 12 q^{46} + 338 q^{49} - 14 q^{52} + 12 q^{55} + 32 q^{58} - 13 q^{61} + 380 q^{64} + 53 q^{67} + 80 q^{70} - 27 q^{73} + 58 q^{76} + 49 q^{79} + 32 q^{82} + 88 q^{88} + 63 q^{91} + 120 q^{94} - 31 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7803))\) 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 17
7803.2.a.a 7803.a 1.a $1$ $62.307$ \(\Q\) None \(-2\) \(0\) \(-2\) \(-4\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}-2q^{5}-4q^{7}+4q^{10}+\cdots\)
7803.2.a.b 7803.a 1.a $1$ $62.307$ \(\Q\) None \(-2\) \(0\) \(-2\) \(-1\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}-2q^{5}-q^{7}+4q^{10}+\cdots\)
7803.2.a.c 7803.a 1.a $1$ $62.307$ \(\Q\) None \(-2\) \(0\) \(2\) \(1\) $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+2q^{5}+q^{7}-4q^{10}+\cdots\)
7803.2.a.d 7803.a 1.a $1$ $62.307$ \(\Q\) None \(-2\) \(0\) \(4\) \(-1\) $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+4q^{5}-q^{7}-8q^{10}+\cdots\)
7803.2.a.e 7803.a 1.a $1$ $62.307$ \(\Q\) None \(-1\) \(0\) \(-4\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-4q^{5}+2q^{7}+3q^{8}+4q^{10}+\cdots\)
7803.2.a.f 7803.a 1.a $1$ $62.307$ \(\Q\) None \(-1\) \(0\) \(-1\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-q^{5}+2q^{7}+3q^{8}+q^{10}+\cdots\)
7803.2.a.g 7803.a 1.a $1$ $62.307$ \(\Q\) None \(-1\) \(0\) \(4\) \(-2\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+4q^{5}-2q^{7}+3q^{8}-4q^{10}+\cdots\)
7803.2.a.h 7803.a 1.a $1$ $62.307$ \(\Q\) None \(0\) \(0\) \(-3\) \(-2\) $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}-3q^{5}-2q^{7}+3q^{11}+2q^{13}+\cdots\)
7803.2.a.i 7803.a 1.a $1$ $62.307$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-5\) $+$ $+$ $N(\mathrm{U}(1))$ \(q-2q^{4}-5q^{7}-7q^{13}+4q^{16}+8q^{19}+\cdots\)
7803.2.a.j 7803.a 1.a $1$ $62.307$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(-4\) $-$ $-$ $N(\mathrm{U}(1))$ \(q-2q^{4}-4q^{7}+2q^{13}+4q^{16}-q^{19}+\cdots\)
7803.2.a.k 7803.a 1.a $1$ $62.307$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(1\) $+$ $+$ $N(\mathrm{U}(1))$ \(q-2q^{4}+q^{7}+5q^{13}+4q^{16}-7q^{19}+\cdots\)
7803.2.a.l 7803.a 1.a $1$ $62.307$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(4\) $+$ $+$ $N(\mathrm{U}(1))$ \(q-2q^{4}+4q^{7}+2q^{13}+4q^{16}-q^{19}+\cdots\)
7803.2.a.m 7803.a 1.a $1$ $62.307$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(5\) $-$ $-$ $N(\mathrm{U}(1))$ \(q-2q^{4}+5q^{7}-7q^{13}+4q^{16}+8q^{19}+\cdots\)
7803.2.a.n 7803.a 1.a $1$ $62.307$ \(\Q\) None \(0\) \(0\) \(3\) \(-2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}+3q^{5}-2q^{7}-3q^{11}+2q^{13}+\cdots\)
7803.2.a.o 7803.a 1.a $1$ $62.307$ \(\Q\) None \(1\) \(0\) \(-4\) \(-2\) $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-4q^{5}-2q^{7}-3q^{8}-4q^{10}+\cdots\)
7803.2.a.p 7803.a 1.a $1$ $62.307$ \(\Q\) None \(1\) \(0\) \(1\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+q^{5}+2q^{7}-3q^{8}+q^{10}+\cdots\)
7803.2.a.q 7803.a 1.a $1$ $62.307$ \(\Q\) None \(1\) \(0\) \(4\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+4q^{5}+2q^{7}-3q^{8}+4q^{10}+\cdots\)
7803.2.a.r 7803.a 1.a $1$ $62.307$ \(\Q\) None \(2\) \(0\) \(-4\) \(-1\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-4q^{5}-q^{7}-8q^{10}+\cdots\)
7803.2.a.s 7803.a 1.a $1$ $62.307$ \(\Q\) None \(2\) \(0\) \(-2\) \(1\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-2q^{5}+q^{7}-4q^{10}+\cdots\)
7803.2.a.t 7803.a 1.a $1$ $62.307$ \(\Q\) None \(2\) \(0\) \(2\) \(-4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+2q^{5}-4q^{7}+4q^{10}+\cdots\)
7803.2.a.u 7803.a 1.a $1$ $62.307$ \(\Q\) None \(2\) \(0\) \(2\) \(-1\) $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+2q^{5}-q^{7}+4q^{10}+\cdots\)
7803.2.a.v 7803.a 1.a $2$ $62.307$ \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(-3\) \(3\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-1+\beta )q^{4}+(-1-\beta )q^{5}+\cdots\)
7803.2.a.w 7803.a 1.a $2$ $62.307$ \(\Q(\sqrt{13}) \) None \(-1\) \(0\) \(5\) \(-3\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(1+\beta )q^{4}+(3-\beta )q^{5}+(-2+\cdots)q^{7}+\cdots\)
7803.2.a.x 7803.a 1.a $2$ $62.307$ \(\Q(\sqrt{17}) \) \(\Q(\sqrt{-51}) \) \(0\) \(0\) \(-3\) \(0\) $+$ $+$ $N(\mathrm{U}(1))$ \(q-2q^{4}+(-1-\beta )q^{5}+(1-2\beta )q^{11}+\cdots\)
7803.2.a.y 7803.a 1.a $2$ $62.307$ \(\Q(\sqrt{17}) \) \(\Q(\sqrt{-51}) \) \(0\) \(0\) \(3\) \(0\) $-$ $+$ $N(\mathrm{U}(1))$ \(q-2q^{4}+(1+\beta )q^{5}+(-1+2\beta )q^{11}+\cdots\)
7803.2.a.z 7803.a 1.a $2$ $62.307$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-8\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-4q^{5}-2\beta q^{7}-2\beta q^{8}-4\beta q^{10}+\cdots\)
7803.2.a.ba 7803.a 1.a $2$ $62.307$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(8\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+4q^{5}+2\beta q^{7}-2\beta q^{8}+4\beta q^{10}+\cdots\)
7803.2.a.bb 7803.a 1.a $2$ $62.307$ \(\Q(\sqrt{5}) \) None \(1\) \(0\) \(3\) \(3\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-1+\beta )q^{4}+(1+\beta )q^{5}+3\beta q^{7}+\cdots\)
7803.2.a.bc 7803.a 1.a $2$ $62.307$ \(\Q(\sqrt{13}) \) None \(1\) \(0\) \(-5\) \(-3\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1+\beta )q^{4}+(-3+\beta )q^{5}+(-2+\cdots)q^{7}+\cdots\)
7803.2.a.bd 7803.a 1.a $3$ $62.307$ 3.3.404.1 None \(-1\) \(0\) \(3\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{2}+(3+\beta _{1}-\beta _{2})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
7803.2.a.be 7803.a 1.a $3$ $62.307$ \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $+$ $-$ $N(\mathrm{U}(1))$ \(q-2q^{4}+(-2\beta _{1}-\beta _{2})q^{7}+(-3\beta _{1}+\cdots)q^{13}+\cdots\)
7803.2.a.bf 7803.a 1.a $3$ $62.307$ \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $-$ $+$ $N(\mathrm{U}(1))$ \(q-2q^{4}+(2\beta _{1}+\beta _{2})q^{7}+(-3\beta _{1}+4\beta _{2})q^{13}+\cdots\)
7803.2.a.bg 7803.a 1.a $3$ $62.307$ 3.3.404.1 None \(1\) \(0\) \(-3\) \(4\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+(3+\beta _{1}-\beta _{2})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
7803.2.a.bh 7803.a 1.a $4$ $62.307$ 4.4.29952.1 None \(0\) \(0\) \(0\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{2}q^{5}-\beta _{3}q^{7}+\cdots\)
7803.2.a.bi 7803.a 1.a $4$ $62.307$ 4.4.29952.1 None \(0\) \(0\) \(0\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{2}q^{5}+\beta _{3}q^{7}+\cdots\)
7803.2.a.bj 7803.a 1.a $5$ $62.307$ 5.5.160801.1 None \(-3\) \(0\) \(-4\) \(1\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{4})q^{2}+(2+\beta _{2}+\beta _{3})q^{4}+\cdots\)
7803.2.a.bk 7803.a 1.a $5$ $62.307$ 5.5.160801.1 None \(-3\) \(0\) \(4\) \(-1\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{4})q^{2}+(2+\beta _{2}+\beta _{3})q^{4}+\cdots\)
7803.2.a.bl 7803.a 1.a $5$ $62.307$ 5.5.160801.1 None \(3\) \(0\) \(-4\) \(-1\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{4})q^{2}+(2+\beta _{2}+\beta _{3})q^{4}+(-1+\cdots)q^{5}+\cdots\)
7803.2.a.bm 7803.a 1.a $5$ $62.307$ 5.5.160801.1 None \(3\) \(0\) \(4\) \(1\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{4})q^{2}+(2+\beta _{2}+\beta _{3})q^{4}+(1+\cdots)q^{5}+\cdots\)
7803.2.a.bn 7803.a 1.a $6$ $62.307$ 6.6.435306496.1 None \(0\) \(0\) \(0\) \(-8\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{5}q^{5}+(-1+\cdots)q^{7}+\cdots\)
7803.2.a.bo 7803.a 1.a $6$ $62.307$ 6.6.435306496.1 None \(0\) \(0\) \(0\) \(8\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{5}q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots\)
7803.2.a.bp 7803.a 1.a $6$ $62.307$ 6.6.1168184448.1 None \(0\) \(0\) \(0\) \(-4\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{3}q^{5}+(-1+\cdots)q^{7}+\cdots\)
7803.2.a.bq 7803.a 1.a $6$ $62.307$ 6.6.1168184448.1 None \(0\) \(0\) \(0\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{3}q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots\)
7803.2.a.br 7803.a 1.a $10$ $62.307$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(-2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{4}q^{5}-\beta _{6}q^{7}+\cdots\)
7803.2.a.bs 7803.a 1.a $10$ $62.307$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(0\) \(0\) \(2\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{4}q^{5}+\beta _{6}q^{7}+\cdots\)
7803.2.a.bt 7803.a 1.a $12$ $62.307$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(-6\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{8}q^{5}+(-1+\cdots)q^{7}+\cdots\)
7803.2.a.bu 7803.a 1.a $12$ $62.307$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(6\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{8}q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots\)
7803.2.a.bv 7803.a 1.a $12$ $62.307$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(-8\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}+\beta _{11})q^{5}+\cdots\)
7803.2.a.bw 7803.a 1.a $12$ $62.307$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(0\) \(8\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{1}-\beta _{11})q^{5}+\cdots\)
7803.2.a.bx 7803.a 1.a $15$ $62.307$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(-6\) \(0\) \(-3\) \(-3\) $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+\beta _{4}q^{5}+(-1+\cdots)q^{7}+\cdots\)
7803.2.a.by 7803.a 1.a $15$ $62.307$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(-6\) \(0\) \(3\) \(3\) $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-\beta _{4}q^{5}+(1+\cdots)q^{7}+\cdots\)
7803.2.a.bz 7803.a 1.a $15$ $62.307$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(6\) \(0\) \(-3\) \(3\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}+\beta _{4}q^{5}+(1+\cdots)q^{7}+\cdots\)
7803.2.a.ca 7803.a 1.a $15$ $62.307$ \(\mathbb{Q}[x]/(x^{15} - \cdots)\) None \(6\) \(0\) \(3\) \(-3\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{4}-\beta _{4}q^{5}+(-1+\cdots)q^{7}+\cdots\)
7803.2.a.cb 7803.a 1.a $18$ $62.307$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(0\) \(0\) \(-6\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{5}q^{5}+(\beta _{7}+\cdots)q^{7}+\cdots\)
7803.2.a.cc 7803.a 1.a $18$ $62.307$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(0\) \(0\) \(0\) \(6\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{5}q^{5}+(-\beta _{7}+\cdots)q^{7}+\cdots\)
7803.2.a.cd 7803.a 1.a $24$ $62.307$ None \(0\) \(0\) \(-20\) \(0\) $-$ $-$ $\mathrm{SU}(2)$
7803.2.a.ce 7803.a 1.a $24$ $62.307$ None \(0\) \(0\) \(0\) \(-16\) $-$ $-$ $\mathrm{SU}(2)$
7803.2.a.cf 7803.a 1.a $24$ $62.307$ None \(0\) \(0\) \(0\) \(16\) $+$ $-$ $\mathrm{SU}(2)$
7803.2.a.cg 7803.a 1.a $24$ $62.307$ None \(0\) \(0\) \(20\) \(0\) $+$ $-$ $\mathrm{SU}(2)$

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7803))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(7803)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(153))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(289))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(459))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(867))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2601))\)\(^{\oplus 2}\)