Properties

Label 2925.2.a
Level $2925$
Weight $2$
Character orbit 2925.a
Rep. character $\chi_{2925}(1,\cdot)$
Character field $\Q$
Dimension $95$
Newform subspaces $43$
Sturm bound $840$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 2925 = 3^{2} \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2925.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 43 \)
Sturm bound: \(840\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(2\), \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2925))\).

Total New Old
Modular forms 444 95 349
Cusp forms 397 95 302
Eisenstein series 47 0 47

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
\(+\)\(+\)\(+\)$+$\(6\)
\(+\)\(+\)\(-\)$-$\(12\)
\(+\)\(-\)\(+\)$-$\(12\)
\(+\)\(-\)\(-\)$+$\(8\)
\(-\)\(+\)\(+\)$-$\(15\)
\(-\)\(+\)\(-\)$+$\(12\)
\(-\)\(-\)\(+\)$+$\(14\)
\(-\)\(-\)\(-\)$-$\(16\)
Plus space\(+\)\(40\)
Minus space\(-\)\(55\)

Trace form

\( 95 q + q^{2} + 101 q^{4} + 4 q^{7} - 3 q^{8} + O(q^{10}) \) \( 95 q + q^{2} + 101 q^{4} + 4 q^{7} - 3 q^{8} + 4 q^{11} + q^{13} - 8 q^{14} + 117 q^{16} + 2 q^{17} + 12 q^{19} + 28 q^{22} - 8 q^{23} + 3 q^{26} + 20 q^{28} + 18 q^{29} - 8 q^{31} + 5 q^{32} + 6 q^{34} + 2 q^{37} - 20 q^{38} - 6 q^{41} + 4 q^{43} - 4 q^{44} + 20 q^{46} - 16 q^{47} + 91 q^{49} + 7 q^{52} + 34 q^{53} + 48 q^{56} - 2 q^{58} - 24 q^{59} + 10 q^{61} + 36 q^{62} + 181 q^{64} + 8 q^{67} - 10 q^{68} - 24 q^{71} + 30 q^{73} + 66 q^{74} + 60 q^{76} + 20 q^{77} + 4 q^{79} - 54 q^{82} - 44 q^{83} + 32 q^{86} + 40 q^{88} + 10 q^{89} + 4 q^{92} - 100 q^{94} + 34 q^{97} - 31 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2925))\) 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
2925.2.a.a 2925.a 1.a $1$ $23.356$ \(\Q\) None \(-2\) \(0\) \(0\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+2q^{4}+2q^{7}-2q^{11}-q^{13}+\cdots\)
2925.2.a.b 2925.a 1.a $1$ $23.356$ \(\Q\) None \(-1\) \(0\) \(0\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-3q^{7}+3q^{8}+q^{11}+q^{13}+\cdots\)
2925.2.a.c 2925.a 1.a $1$ $23.356$ \(\Q\) None \(-1\) \(0\) \(0\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-2q^{7}+3q^{8}+4q^{11}+\cdots\)
2925.2.a.d 2925.a 1.a $1$ $23.356$ \(\Q\) None \(-1\) \(0\) \(0\) \(0\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+3q^{8}-4q^{11}-q^{13}+\cdots\)
2925.2.a.e 2925.a 1.a $1$ $23.356$ \(\Q\) None \(-1\) \(0\) \(0\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+q^{7}+3q^{8}+q^{11}+q^{13}+\cdots\)
2925.2.a.f 2925.a 1.a $1$ $23.356$ \(\Q\) None \(-1\) \(0\) \(0\) \(4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}+4q^{7}+3q^{8}-2q^{11}+\cdots\)
2925.2.a.g 2925.a 1.a $1$ $23.356$ \(\Q\) None \(0\) \(0\) \(0\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}-4q^{7}+6q^{11}+q^{13}+4q^{16}+\cdots\)
2925.2.a.h 2925.a 1.a $1$ $23.356$ \(\Q\) None \(0\) \(0\) \(0\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}-q^{7}+q^{11}-q^{13}+4q^{16}+\cdots\)
2925.2.a.i 2925.a 1.a $1$ $23.356$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}+q^{7}-3q^{11}-q^{13}+4q^{16}+\cdots\)
2925.2.a.j 2925.a 1.a $1$ $23.356$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{4}+q^{7}+q^{11}+q^{13}+4q^{16}+\cdots\)
2925.2.a.k 2925.a 1.a $1$ $23.356$ \(\Q\) None \(0\) \(0\) \(0\) \(1\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}+q^{7}+3q^{11}-q^{13}+4q^{16}+\cdots\)
2925.2.a.l 2925.a 1.a $1$ $23.356$ \(\Q\) None \(0\) \(0\) \(0\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{4}+4q^{7}+6q^{11}-q^{13}+4q^{16}+\cdots\)
2925.2.a.m 2925.a 1.a $1$ $23.356$ \(\Q\) None \(1\) \(0\) \(0\) \(-2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-2q^{7}-3q^{8}-4q^{11}+\cdots\)
2925.2.a.n 2925.a 1.a $1$ $23.356$ \(\Q\) None \(1\) \(0\) \(0\) \(-1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}-q^{7}-3q^{8}+q^{11}-q^{13}+\cdots\)
2925.2.a.o 2925.a 1.a $1$ $23.356$ \(\Q\) None \(1\) \(0\) \(0\) \(3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+3q^{7}-3q^{8}+q^{11}-q^{13}+\cdots\)
2925.2.a.p 2925.a 1.a $1$ $23.356$ \(\Q\) None \(1\) \(0\) \(0\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+4q^{7}-3q^{8}-4q^{11}+\cdots\)
2925.2.a.q 2925.a 1.a $1$ $23.356$ \(\Q\) None \(2\) \(0\) \(0\) \(-3\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-3q^{7}+q^{11}+q^{13}+\cdots\)
2925.2.a.r 2925.a 1.a $1$ $23.356$ \(\Q\) None \(2\) \(0\) \(0\) \(-2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}-2q^{7}-2q^{11}+q^{13}+\cdots\)
2925.2.a.s 2925.a 1.a $1$ $23.356$ \(\Q\) None \(2\) \(0\) \(0\) \(1\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+q^{7}-5q^{11}+q^{13}+\cdots\)
2925.2.a.t 2925.a 1.a $1$ $23.356$ \(\Q\) None \(2\) \(0\) \(0\) \(3\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+3q^{7}+5q^{11}-q^{13}+\cdots\)
2925.2.a.u 2925.a 1.a $2$ $23.356$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+(-2+2\beta )q^{7}+\cdots\)
2925.2.a.v 2925.a 1.a $2$ $23.356$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}-2\beta q^{7}+\cdots\)
2925.2.a.w 2925.a 1.a $2$ $23.356$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+(1-\beta )q^{7}+\cdots\)
2925.2.a.x 2925.a 1.a $2$ $23.356$ \(\Q(\sqrt{17}) \) None \(-1\) \(0\) \(0\) \(5\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(2+\beta )q^{4}+(3-\beta )q^{7}+(-4+\cdots)q^{8}+\cdots\)
2925.2.a.y 2925.a 1.a $2$ $23.356$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(-4\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{4}-2q^{7}-\beta q^{8}+2\beta q^{11}+\cdots\)
2925.2.a.z 2925.a 1.a $2$ $23.356$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(-4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{4}-2q^{7}-\beta q^{8}+(3-\beta )q^{11}+\cdots\)
2925.2.a.ba 2925.a 1.a $2$ $23.356$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{4}-q^{7}-\beta q^{8}+\beta q^{11}+\cdots\)
2925.2.a.bb 2925.a 1.a $2$ $23.356$ \(\Q(\sqrt{3}) \) None \(0\) \(0\) \(0\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{4}+q^{7}-\beta q^{8}-\beta q^{11}+\cdots\)
2925.2.a.bc 2925.a 1.a $2$ $23.356$ \(\Q(\sqrt{17}) \) None \(1\) \(0\) \(0\) \(5\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(2+\beta )q^{4}+(3-\beta )q^{7}+(4+\beta )q^{8}+\cdots\)
2925.2.a.bd 2925.a 1.a $2$ $23.356$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(-2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+(-1-\beta )q^{7}+\cdots\)
2925.2.a.be 2925.a 1.a $3$ $23.356$ 3.3.148.1 None \(-3\) \(0\) \(0\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
2925.2.a.bf 2925.a 1.a $3$ $23.356$ 3.3.148.1 None \(-3\) \(0\) \(0\) \(2\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+\cdots\)
2925.2.a.bg 2925.a 1.a $3$ $23.356$ 3.3.564.1 None \(-1\) \(0\) \(0\) \(5\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(2-\beta _{1})q^{7}+\cdots\)
2925.2.a.bh 2925.a 1.a $3$ $23.356$ 3.3.316.1 None \(0\) \(0\) \(0\) \(-1\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(3+\beta _{2})q^{4}+\beta _{2}q^{7}+(2-3\beta _{1}+\cdots)q^{8}+\cdots\)
2925.2.a.bi 2925.a 1.a $3$ $23.356$ 3.3.564.1 None \(1\) \(0\) \(0\) \(-5\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-2+\beta _{1})q^{7}+\cdots\)
2925.2.a.bj 2925.a 1.a $3$ $23.356$ 3.3.148.1 None \(3\) \(0\) \(0\) \(-2\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(-1+\cdots)q^{7}+\cdots\)
2925.2.a.bk 2925.a 1.a $3$ $23.356$ 3.3.148.1 None \(3\) \(0\) \(0\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2})q^{4}+(1+\cdots)q^{7}+\cdots\)
2925.2.a.bl 2925.a 1.a $5$ $23.356$ 5.5.1821184.1 None \(0\) \(0\) \(0\) \(-5\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1+\beta _{1}-\beta _{4})q^{7}+\cdots\)
2925.2.a.bm 2925.a 1.a $5$ $23.356$ 5.5.1821184.1 None \(0\) \(0\) \(0\) \(5\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(1-\beta _{1}+\beta _{4})q^{7}+\cdots\)
2925.2.a.bn 2925.a 1.a $6$ $23.356$ 6.6.12730624.1 None \(0\) \(0\) \(0\) \(-10\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-2-\beta _{2}-\beta _{5})q^{7}+\cdots\)
2925.2.a.bo 2925.a 1.a $6$ $23.356$ 6.6.12730624.1 None \(0\) \(0\) \(0\) \(10\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(2+\beta _{2}+\beta _{5})q^{7}+\cdots\)
2925.2.a.bp 2925.a 1.a $6$ $23.356$ 6.6.1509051136.3 None \(0\) \(0\) \(0\) \(-6\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(-1-\beta _{4})q^{7}+\cdots\)
2925.2.a.bq 2925.a 1.a $6$ $23.356$ 6.6.1509051136.3 None \(0\) \(0\) \(0\) \(6\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+(1+\beta _{4})q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2925))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(2925)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(39))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(117))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(195))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(225))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(325))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(585))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(975))\)\(^{\oplus 2}\)