Properties

Label 2601.2.a
Level $2601$
Weight $2$
Character orbit 2601.a
Rep. character $\chi_{2601}(1,\cdot)$
Character field $\Q$
Dimension $106$
Newform subspaces $38$
Sturm bound $612$
Trace bound $73$

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Defining parameters

Level: \( N \) \(=\) \( 2601 = 3^{2} \cdot 17^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2601.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 38 \)
Sturm bound: \(612\)
Trace bound: \(73\)
Distinguishing \(T_p\): \(2\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2601))\).

Total New Old
Modular forms 342 121 221
Cusp forms 271 106 165
Eisenstein series 71 15 56

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.
\(+\)\(+\)\(+\)\(19\)
\(+\)\(-\)\(-\)\(27\)
\(-\)\(+\)\(-\)\(32\)
\(-\)\(-\)\(+\)\(28\)
Plus space\(+\)\(47\)
Minus space\(-\)\(59\)

Trace form

\( 106 q - 2 q^{2} + 98 q^{4} + 4 q^{5} + 4 q^{7} - 6 q^{8} + O(q^{10}) \) \( 106 q - 2 q^{2} + 98 q^{4} + 4 q^{5} + 4 q^{7} - 6 q^{8} + 4 q^{10} - 4 q^{11} + 6 q^{13} - 4 q^{14} + 90 q^{16} + 2 q^{19} + 12 q^{20} - 4 q^{22} + 4 q^{23} + 80 q^{25} + 4 q^{26} + 4 q^{28} + 12 q^{29} - 12 q^{31} - 24 q^{32} - 12 q^{37} + 64 q^{38} + 28 q^{40} - 12 q^{41} + 6 q^{43} + 12 q^{44} - 20 q^{46} - 18 q^{47} + 68 q^{49} - 32 q^{50} - 12 q^{52} + 6 q^{53} - 14 q^{55} + 12 q^{56} - 4 q^{58} + 6 q^{59} - 12 q^{61} - 20 q^{62} + 54 q^{64} - 22 q^{67} - 8 q^{70} + 12 q^{71} + 12 q^{73} + 20 q^{74} - 4 q^{76} + 2 q^{77} + 4 q^{79} + 44 q^{80} + 20 q^{82} - 20 q^{83} - 18 q^{86} + 4 q^{88} + 22 q^{89} - 16 q^{91} - 36 q^{92} - 80 q^{94} - 16 q^{95} + 12 q^{97} + 12 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2601))\) 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
2601.2.a.a 2601.a 1.a $1$ $20.769$ \(\Q\) None \(-2\) \(0\) \(-3\) \(-2\) $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}-3q^{5}-2q^{7}+6q^{10}+\cdots\)
2601.2.a.b 2601.a 1.a $1$ $20.769$ \(\Q\) None \(-2\) \(0\) \(1\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+q^{5}+2q^{7}-2q^{10}+\cdots\)
2601.2.a.c 2601.a 1.a $1$ $20.769$ \(\Q\) None \(-2\) \(0\) \(3\) \(2\) $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+3q^{5}+2q^{7}-6q^{10}+\cdots\)
2601.2.a.d 2601.a 1.a $1$ $20.769$ \(\Q\) None \(-1\) \(0\) \(-2\) \(1\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-2q^{5}+q^{7}+3q^{8}+2q^{10}+\cdots\)
2601.2.a.e 2601.a 1.a $1$ $20.769$ \(\Q\) None \(-1\) \(0\) \(2\) \(-1\) $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+2q^{5}-q^{7}+3q^{8}-2q^{10}+\cdots\)
2601.2.a.f 2601.a 1.a $1$ $20.769$ \(\Q\) None \(0\) \(0\) \(3\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}+3q^{5}+4q^{7}-3q^{11}-q^{13}+\cdots\)
2601.2.a.g 2601.a 1.a $1$ $20.769$ \(\Q\) None \(1\) \(0\) \(-2\) \(-4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-2q^{5}-4q^{7}-3q^{8}-2q^{10}+\cdots\)
2601.2.a.h 2601.a 1.a $1$ $20.769$ \(\Q\) None \(1\) \(0\) \(-2\) \(-1\) $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-2q^{5}-q^{7}-3q^{8}-2q^{10}+\cdots\)
2601.2.a.i 2601.a 1.a $1$ $20.769$ \(\Q\) None \(1\) \(0\) \(0\) \(-4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-4q^{7}-3q^{8}-4q^{11}+\cdots\)
2601.2.a.j 2601.a 1.a $1$ $20.769$ \(\Q\) None \(1\) \(0\) \(0\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+4q^{7}-3q^{8}+4q^{11}+\cdots\)
2601.2.a.k 2601.a 1.a $1$ $20.769$ \(\Q\) None \(1\) \(0\) \(2\) \(1\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+2q^{5}+q^{7}-3q^{8}+2q^{10}+\cdots\)
2601.2.a.l 2601.a 1.a $1$ $20.769$ \(\Q\) None \(2\) \(0\) \(-1\) \(2\) $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-q^{5}+2q^{7}-2q^{10}+\cdots\)
2601.2.a.m 2601.a 1.a $2$ $20.769$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(-6\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+2\beta q^{5}+\cdots\)
2601.2.a.n 2601.a 1.a $2$ $20.769$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(6\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}-2\beta q^{5}+\cdots\)
2601.2.a.o 2601.a 1.a $2$ $20.769$ \(\Q(\sqrt{17}) \) \(\Q(\sqrt{-51}) \) \(0\) \(0\) \(0\) \(0\) $+$ $+$ $N(\mathrm{U}(1))$ \(q-2q^{4}-\beta q^{5}+\beta q^{11}-q^{13}+4q^{16}+\cdots\)
2601.2.a.p 2601.a 1.a $2$ $20.769$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(-2\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}-q^{5}+\beta q^{7}-2\beta q^{8}-\beta q^{10}+\cdots\)
2601.2.a.q 2601.a 1.a $2$ $20.769$ \(\Q(\sqrt{2}) \) None \(0\) \(0\) \(2\) \(0\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{5}-\beta q^{7}-2\beta q^{8}+\beta q^{10}+\cdots\)
2601.2.a.r 2601.a 1.a $2$ $20.769$ \(\Q(\sqrt{13}) \) None \(1\) \(0\) \(-1\) \(3\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1+\beta )q^{4}-\beta q^{5}+(2-\beta )q^{7}+\cdots\)
2601.2.a.s 2601.a 1.a $2$ $20.769$ \(\Q(\sqrt{13}) \) None \(1\) \(0\) \(1\) \(-3\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1+\beta )q^{4}+\beta q^{5}+(-2+\beta )q^{7}+\cdots\)
2601.2.a.t 2601.a 1.a $2$ $20.769$ \(\Q(\sqrt{17}) \) None \(1\) \(0\) \(3\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(2+\beta )q^{4}+(1+\beta )q^{5}+(4+\beta )q^{8}+\cdots\)
2601.2.a.u 2601.a 1.a $3$ $20.769$ \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $+$ $+$ $N(\mathrm{U}(1))$ \(q-2q^{4}+(3\beta _{1}-\beta _{2})q^{7}+(-4\beta _{1}+3\beta _{2})q^{13}+\cdots\)
2601.2.a.v 2601.a 1.a $3$ $20.769$ \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(0\) $+$ $-$ $N(\mathrm{U}(1))$ \(q-2q^{4}+(-3\beta _{1}+\beta _{2})q^{7}+(-4\beta _{1}+\cdots)q^{13}+\cdots\)
2601.2.a.w 2601.a 1.a $3$ $20.769$ \(\Q(\zeta_{18})^+\) None \(0\) \(0\) \(-6\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-2+\beta _{1})q^{5}-\beta _{2}q^{7}+\cdots\)
2601.2.a.x 2601.a 1.a $3$ $20.769$ \(\Q(\zeta_{18})^+\) None \(0\) \(0\) \(6\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(2-\beta _{1})q^{5}+\beta _{2}q^{7}+\cdots\)
2601.2.a.y 2601.a 1.a $3$ $20.769$ \(\Q(\zeta_{18})^+\) None \(3\) \(0\) \(-3\) \(3\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
2601.2.a.z 2601.a 1.a $3$ $20.769$ \(\Q(\zeta_{18})^+\) None \(3\) \(0\) \(3\) \(-3\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
2601.2.a.ba 2601.a 1.a $4$ $20.769$ \(\Q(\zeta_{16})^+\) None \(-4\) \(0\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+(-\beta _{1}-2\beta _{3})q^{5}+2\beta _{1}q^{7}+\cdots\)
2601.2.a.bb 2601.a 1.a $4$ $20.769$ \(\Q(\zeta_{16})^+\) None \(-4\) \(0\) \(0\) \(0\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+(1+2\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots\)
2601.2.a.bc 2601.a 1.a $4$ $20.769$ \(\Q(\zeta_{16})^+\) None \(0\) \(0\) \(-4\) \(8\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-1+\beta _{1}+\beta _{3})q^{5}+\cdots\)
2601.2.a.bd 2601.a 1.a $4$ $20.769$ \(\Q(\zeta_{16})^+\) None \(0\) \(0\) \(4\) \(-8\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(1-\beta _{1}-\beta _{3})q^{5}+\cdots\)
2601.2.a.be 2601.a 1.a $4$ $20.769$ 4.4.7232.1 None \(2\) \(0\) \(-6\) \(4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(\beta _{1}-\beta _{3})q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
2601.2.a.bf 2601.a 1.a $4$ $20.769$ 4.4.7232.1 None \(2\) \(0\) \(6\) \(-4\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(\beta _{1}-\beta _{3})q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(1+\cdots)q^{5}+\cdots\)
2601.2.a.bg 2601.a 1.a $4$ $20.769$ \(\Q(\zeta_{16})^+\) None \(4\) \(0\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+(-\beta _{1}-2\beta _{3})q^{5}-2\beta _{1}q^{7}+\cdots\)
2601.2.a.bh 2601.a 1.a $6$ $20.769$ 6.6.3418281.1 None \(-3\) \(0\) \(-3\) \(-3\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{4}q^{2}+(1+\beta _{1}+\beta _{2}-\beta _{4}+2\beta _{5})q^{4}+\cdots\)
2601.2.a.bi 2601.a 1.a $6$ $20.769$ 6.6.3418281.1 None \(-3\) \(0\) \(3\) \(3\) $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{4}q^{2}+(1+\beta _{1}+\beta _{2}-\beta _{4}+2\beta _{5})q^{4}+\cdots\)
2601.2.a.bj 2601.a 1.a $6$ $20.769$ 6.6.45769536.1 None \(0\) \(0\) \(0\) \(-18\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(3+\beta _{2})q^{4}-\beta _{3}q^{5}+(-3+\cdots)q^{7}+\cdots\)
2601.2.a.bk 2601.a 1.a $6$ $20.769$ 6.6.45769536.1 None \(0\) \(0\) \(0\) \(18\) $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(3+\beta _{2})q^{4}+\beta _{3}q^{5}+(3-\beta _{2}+\cdots)q^{7}+\cdots\)
2601.2.a.bl 2601.a 1.a $8$ $20.769$ 8.8.4848615424.1 None \(0\) \(0\) \(0\) \(0\) $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{4}q^{2}+(4-\beta _{2})q^{4}-\beta _{1}q^{5}+(\beta _{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2601))\) into lower level spaces

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