Properties

Label 3150.2.a
Level $3150$
Weight $2$
Character orbit 3150.a
Rep. character $\chi_{3150}(1,\cdot)$
Character field $\Q$
Dimension $48$
Newform subspaces $46$
Sturm bound $1440$
Trace bound $17$

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Defining parameters

Level: \( N \) \(=\) \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3150.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 46 \)
Sturm bound: \(1440\)
Trace bound: \(17\)
Distinguishing \(T_p\): \(11\), \(13\), \(17\), \(19\), \(29\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3150))\).

Total New Old
Modular forms 768 48 720
Cusp forms 673 48 625
Eisenstein series 95 0 95

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

\(2\)\(3\)\(5\)\(7\)FrickeDim.
\(+\)\(+\)\(+\)\(+\)\(+\)\(2\)
\(+\)\(+\)\(+\)\(-\)\(-\)\(2\)
\(+\)\(+\)\(-\)\(+\)\(-\)\(3\)
\(+\)\(+\)\(-\)\(-\)\(+\)\(3\)
\(+\)\(-\)\(+\)\(+\)\(-\)\(3\)
\(+\)\(-\)\(+\)\(-\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(+\)\(+\)\(3\)
\(+\)\(-\)\(-\)\(-\)\(-\)\(5\)
\(-\)\(+\)\(+\)\(+\)\(-\)\(2\)
\(-\)\(+\)\(+\)\(-\)\(+\)\(2\)
\(-\)\(+\)\(-\)\(+\)\(+\)\(3\)
\(-\)\(+\)\(-\)\(-\)\(-\)\(3\)
\(-\)\(-\)\(+\)\(+\)\(+\)\(4\)
\(-\)\(-\)\(+\)\(-\)\(-\)\(5\)
\(-\)\(-\)\(-\)\(+\)\(-\)\(4\)
\(-\)\(-\)\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(21\)
Minus space\(-\)\(27\)

Trace form

\( 48q + 2q^{2} + 48q^{4} + 2q^{8} + O(q^{10}) \) \( 48q + 2q^{2} + 48q^{4} + 2q^{8} - 8q^{11} - 10q^{13} - 2q^{14} + 48q^{16} - 4q^{17} - 18q^{19} - 12q^{22} - 16q^{23} - 18q^{26} - 12q^{29} + 4q^{31} + 2q^{32} - 28q^{34} + 12q^{37} - 18q^{38} - 40q^{41} - 4q^{43} - 8q^{44} - 8q^{46} - 20q^{47} + 48q^{49} - 10q^{52} + 16q^{53} - 2q^{56} + 8q^{58} + 14q^{59} - 10q^{61} + 12q^{62} + 48q^{64} - 8q^{67} - 4q^{68} + 80q^{71} + 8q^{73} - 40q^{74} - 18q^{76} + 12q^{77} + 16q^{79} + 32q^{82} + 18q^{83} + 28q^{86} - 12q^{88} + 100q^{89} + 18q^{91} - 16q^{92} + 12q^{94} + 20q^{97} + 2q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3150))\) into newform subspaces

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3 5 7
3150.2.a.a \(1\) \(25.153\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}-6q^{11}+q^{13}+\cdots\)
3150.2.a.b \(1\) \(25.153\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}-4q^{11}-3q^{13}+\cdots\)
3150.2.a.c \(1\) \(25.153\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}-2q^{11}+q^{13}+\cdots\)
3150.2.a.d \(1\) \(25.153\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}-2q^{11}+6q^{13}+\cdots\)
3150.2.a.e \(1\) \(25.153\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}-4q^{13}+q^{14}+\cdots\)
3150.2.a.f \(1\) \(25.153\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}-2q^{13}+q^{14}+\cdots\)
3150.2.a.g \(1\) \(25.153\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}-2q^{13}+q^{14}+\cdots\)
3150.2.a.h \(1\) \(25.153\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(+\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}+q^{13}+q^{14}+\cdots\)
3150.2.a.i \(1\) \(25.153\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(-\) \(+\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}+4q^{13}+q^{14}+\cdots\)
3150.2.a.j \(1\) \(25.153\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(-\) \(-\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}+5q^{11}-6q^{13}+\cdots\)
3150.2.a.k \(1\) \(25.153\) \(\Q\) None \(-1\) \(0\) \(0\) \(-1\) \(+\) \(+\) \(-\) \(+\) \(q-q^{2}+q^{4}-q^{7}-q^{8}+6q^{11}+2q^{13}+\cdots\)
3150.2.a.l \(1\) \(25.153\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}-6q^{11}-2q^{13}+\cdots\)
3150.2.a.m \(1\) \(25.153\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}-3q^{11}+2q^{13}+\cdots\)
3150.2.a.n \(1\) \(25.153\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}-2q^{11}-q^{13}+\cdots\)
3150.2.a.o \(1\) \(25.153\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}-q^{13}-q^{14}+\cdots\)
3150.2.a.p \(1\) \(25.153\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(+\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}+4q^{13}-q^{14}+\cdots\)
3150.2.a.q \(1\) \(25.153\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}+2q^{11}+2q^{13}+\cdots\)
3150.2.a.r \(1\) \(25.153\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}+2q^{11}+7q^{13}+\cdots\)
3150.2.a.s \(1\) \(25.153\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}+4q^{11}-6q^{13}+\cdots\)
3150.2.a.t \(1\) \(25.153\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(-\) \(+\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}+4q^{11}+2q^{13}+\cdots\)
3150.2.a.u \(1\) \(25.153\) \(\Q\) None \(-1\) \(0\) \(0\) \(1\) \(+\) \(+\) \(+\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}+4q^{11}+3q^{13}+\cdots\)
3150.2.a.v \(1\) \(25.153\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}-6q^{11}+2q^{13}+\cdots\)
3150.2.a.w \(1\) \(25.153\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}-4q^{11}+2q^{13}+\cdots\)
3150.2.a.x \(1\) \(25.153\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}-3q^{11}-2q^{13}+\cdots\)
3150.2.a.y \(1\) \(25.153\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}-2q^{11}+q^{13}+\cdots\)
3150.2.a.z \(1\) \(25.153\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}-4q^{13}-q^{14}+\cdots\)
3150.2.a.ba \(1\) \(25.153\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}-2q^{13}-q^{14}+\cdots\)
3150.2.a.bb \(1\) \(25.153\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}-2q^{13}-q^{14}+\cdots\)
3150.2.a.bc \(1\) \(25.153\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(+\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}+q^{13}-q^{14}+\cdots\)
3150.2.a.bd \(1\) \(25.153\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(-\) \(+\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}+2q^{11}-7q^{13}+\cdots\)
3150.2.a.be \(1\) \(25.153\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}+2q^{11}-2q^{13}+\cdots\)
3150.2.a.bf \(1\) \(25.153\) \(\Q\) None \(1\) \(0\) \(0\) \(-1\) \(-\) \(+\) \(-\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}+4q^{11}-3q^{13}+\cdots\)
3150.2.a.bg \(1\) \(25.153\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}-6q^{11}-q^{13}+\cdots\)
3150.2.a.bh \(1\) \(25.153\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}-4q^{11}-6q^{13}+\cdots\)
3150.2.a.bi \(1\) \(25.153\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(+\) \(+\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}-4q^{11}+3q^{13}+\cdots\)
3150.2.a.bj \(1\) \(25.153\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}-4q^{11}+6q^{13}+\cdots\)
3150.2.a.bk \(1\) \(25.153\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(-\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}-2q^{11}-6q^{13}+\cdots\)
3150.2.a.bl \(1\) \(25.153\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}-2q^{11}-q^{13}+\cdots\)
3150.2.a.bm \(1\) \(25.153\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}-q^{13}+q^{14}+\cdots\)
3150.2.a.bn \(1\) \(25.153\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}+4q^{13}+q^{14}+\cdots\)
3150.2.a.bo \(1\) \(25.153\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}+4q^{11}-6q^{13}+\cdots\)
3150.2.a.bp \(1\) \(25.153\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}+4q^{11}+2q^{13}+\cdots\)
3150.2.a.bq \(1\) \(25.153\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(-\) \(+\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}+5q^{11}+6q^{13}+\cdots\)
3150.2.a.br \(1\) \(25.153\) \(\Q\) None \(1\) \(0\) \(0\) \(1\) \(-\) \(+\) \(-\) \(-\) \(q+q^{2}+q^{4}+q^{7}+q^{8}+6q^{11}-2q^{13}+\cdots\)
3150.2.a.bs \(2\) \(25.153\) \(\Q(\sqrt{6}) \) None \(-2\) \(0\) \(0\) \(2\) \(+\) \(-\) \(-\) \(-\) \(q-q^{2}+q^{4}+q^{7}-q^{8}+2\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
3150.2.a.bt \(2\) \(25.153\) \(\Q(\sqrt{6}) \) None \(2\) \(0\) \(0\) \(-2\) \(-\) \(-\) \(-\) \(+\) \(q+q^{2}+q^{4}-q^{7}+q^{8}+2\beta q^{11}+(2+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3150))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_0(3150)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(175))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(210))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(225))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(315))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(350))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(450))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(525))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(630))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1050))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1575))\)\(^{\oplus 2}\)